how to find the circumcenter of a triangle

Step-by-step explanation: Given Y is the circumcenter of ΔSTU. How can I find the circumcenter of a triangle in R 3? Find the vertex opposite to the longest side and set it as the orthocenter. The circumcenter of an acute angled triangle lies inside the triangle. I am trying to find the circumcenter of a triangle with python and no external libraries for a geometry calculator that I am making. Use the “Angle Bisector” tool to find the incenter of the triangle. Method to calculate the circumcenter of a triangle. Steps to construct the circumcenter of a triangle: Step 1: Draw the perpendicular bisectors of all the sides of the triangle using a compass.. Find the circumcenter of the triangle. The point of concurrency is not necessarily inside the triangle. How does the circumcenter change as the triangle changes? Permalink. Next you … The circumcenter was constructed by identifying the midpoints of (-1, 1) (4,-2) (-1, -2) 1 See answer Ikgolden is waiting for your help. New Resources. The circumcenter is found as a step to constructing the circumcircle. Step 1 : This particular example is of an acute scalene triangle. The point of concurrency of the perpendicular bisectors of the sides is called the circumcenter of the triangle. asking yourself, “What does circumscribed mean?”  Let’s look at the picture of our triangle and Here \(\text{OA = OB = OC}\), these are the radii of the circle. The thing is I can't use equations such as y=mx+b because the computer thinks that I am trying to define a variable rather than doing algebra. * Calculate the circumcentre of a triangle, if coordinates of vertices are given. perpendicular bisectors of the sides of a triangle. See Construction of the Circumcircle of a Triangle has an animated demonstration of the technique, and a worksheet to try it yourself. Step 1 : Find the equations of the perpendicular bisectors of any two sides of the triangle. 8). Consider the points of the sides to be x1,y1 and x2,y2 respectively. Follow edited Aug 8 '18 at 3:42. It may actually be in the triangle, on the triangle, or outside of the triangle. We need to find the equation of the perpendicular bisectors to find the points of the Circumcenter. You find a triangle’s circumcenter at the intersection of the perpendicular bisectors of the triangle’s sides. triangles. Steps to construct the circumcenter of a triangle: Step 1: Draw the perpendicular bisectors of all the sides of the triangle using a compass.. Calculate the distance between them and prit it as the result. Thus, each side of the triangle is a chord of the circle. It is also the center of the circumcircle, the circle that passes through all three vertices of the triangle.This page shows how to construct (draw) the circumcenter of a triangle with compass and straightedge or ruler. You might want a … Triangle Centers. Find the circumcenter of a triangle with the give… 02:43 View Full Video. TN = 22 units. Step:2 Calculate the slope of each side. In other words, the point of concurrency of the bisector of the sides of a triangle is called the circumcenter. For example, There points A (1, 3), B (5, 5), C (7, 5), the circumcenter is(6, -2). Then knowing that all three of the new lines have to meet up at the same point, you find your circumcenter. Does the circumcenter always lie inside the triangle? Image will be added soon. also note where the circumcenter gets its name. Since the center of the circumscribed circle lies on the hypotenuse, the hypotenuse becomes the diameter of the circle. The point where they intersect is the circumcenter. Below is the implementation of the above approach: Given points are, A = (2,1), B = (-2, 3), C = (1, -2) To find out the circumcentre we have to solve any two bisector equations and find out the intersection points. The Jump To Question Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 … circumscribed inside of. How does the Perpendicular Bisector Theorem, and its converse, help us show that the perpendicular bisectors of a triangle must intersect at the same point? O is the circumcenter of triangle ABC. The circumcenter of an obtuse isosceles triangle is outside the triangle and the perpendicular bisector passes through the obtuse angle of the triangle. OA=OB because O is on the bisector of AB. From our first statement we Methods to Calculate Circumcenter of Triangle. When does the circumcenter lie outside the triangle? Let’s now explore what happens to the Step:1 Find the coordinates of midpoint (x m, y m), of sides AB, BC and AC, using the mid-point theorem. You may find the manual calculation of circumcenter very difficult because it involves complicated equations and concepts. The circumcenter of a triangle is the perpendicular bisectors meet. For this we will be provided with three noncollinear points. By say the vector (m,n) Then the circumcenter would be at (m, n + (b² - a²)/2b) Use 2 points at a time. Already have an account? We need to find the equation of the perpendicular bisectors to find the points of the Circumcenter. the hypotenuse. The circumcenter is the point which is the same distance away from all 3 vertexes of the triangle. A few more questions for … Note: This tutorial explains the ins and outs of the circumcenter of a triangle. Note here that, there is no need to find all of the three sides of the triangle. equidistant from the three vertices of the triangle. After getting these, we can find the circumcenter of the triangle by a simple property stated as under: The circumcenter of the triangle is point where all the perpendicular bisectors of the sides of the triangle intersect. Consider the points of the sides to be x1,y1 and x2,y2 respectively. from two points lies on the perpendicular bisector of the segment determined by Like. Now Properties of Circumcenter of Triangle. It is not a triangle either, it becomes a polyhedra. Remember that the perpendicular bisectors of the sides of a triangle may not necessarily pass through the vertices of the triangle. Share. area = … Then based on that, you can find the slope of the three lines that are perpendicular to the three lines used to make the triangle that goes through the mid-point of the original line, so we can create an equation for these three new lines. The circumcenter is the intersection point of the perpendicular bisectors of the sides. circumcenter to each vertex is a radii of the circle. Code to add this calci to your website . The circumcenter of a right triangle is right at the mid point aka where 4-2 is New questions in Mathematics. Report. See Construction of the Circumcircle of a Triangle has an animated demonstration of the technique, and a worksheet to try it yourself. You'll see how to build up from the Perpendicular Bisector Theorem to find the circumcenter of a triangle. Find the coordinates of the circumcentre of the triangle whose vertices are: (5, -3), (3, -1), (-1, 5) Hi Kathryn. Let’s The circumcenter is also the center of circle that the triangle is The point of concurrency is not necessarily inside the triangle. Q.E.D. Notice is outside the triangle and the perpendicular bisector passes through the y-y 1 = m (x-x 1) Get the equation of all remaining lines using their midpoints and slope. Step 2: Extend all the perpendicular bisectors to meet at a point.Mark the intersection point as \(\text O \), this is the circumcenter. Since the radii of the circle are congruent, a circumcenter is equidistant from vertices of the triangle. circumcenter of a right triangle is the midpoint F of hypotenuse AB (coordinates of the midpoint of a segment are the mean of the coordinates of its vertices) F(9,12) centroid G of any triangle has coordinates which are the mean of the coordinates of triangle's vertices, G(6,8) incenter H is the center of inscribed circle, whose radius is. Virtual Nerd's patent-pending tutorial system provides in-context information, hints, and links to supporting tutorials, synchronized with videos, each 3 to 7 minutes long. The solution (x, y) is the circumcenter of the triangle given. It may actually be in the triangle, on the triangle, or outside of the triangle. Find the longest of the three sides of the right-angled triangle, i.e. Topical Outline | Geometry Outline | Let the points of the sides be A(5,7), B(6,6) and C(2,-2). It is the center of the circle circumscribed about the triangle, making the circumcenter equidistant from the three vertices of the triangle. The CIRCUMCENTER of a triangle is the point in the plane Note: Circumcenter of a triangle is the centre of the circle, formed by the three vertices of a triangle. Simply construct the perpendicular bisectors for all three sides of the triangle. It is also the center of the circumcircle, the circle that passes through all three vertices of the triangle.This page shows how to construct (draw) the circumcenter of a triangle … It may actually be in the triangle, on the triangle, or outside of the triangle. Move the corners of the triangle around to show how the circumcenter and incenter move. Medians are lines that pass through the midpoint of two of the triangle's points and opposite vertex of a triangle. The circumradius of a cyclic polygon is a radius of the circle inside which the … from this site to the Internet Answer:To find the circumcenter of any triangle, find the perpendicular bisectors of the sides and extend them. For each of those, the "center" is where special lines cross, so it all depends on those lines! circumcenter of an obtuse isosceles triangle The point at which the perpendicular intersects … Find the slope of line. Since a point equidistant Report. Then perpendicular bisectors of the triangle lines, Last Solve any two pair of equations, The intersection point is the circumcenter. Construct a circle circumscribed about a triangle. MathBitsNotebook.com The point of concurrency of the perpendicular bisectors of the sides is called the circumcenter of the triangle. I am attending grammar school and we are dealing with vectors. This tutorial shows you how to find the incenter of a triangle by first finding the angle bisectors. Calculate the circumcenter of a triangle from the known values of 3 sets of X,Y co-ordinates. 6x - 56 = 3x - 17 . This is well explained in the following diagram. So find the point halfway between XY, and find the slope of XY. Find the center of the hypotenuse and set it as the circumcenter. the circle. In Geometry, a circumcenter is defined as a point where the perpendicular bisectors of three sides of a triangle intersect. the segments AC, CD, and DA. We have seen how to construct perpendicular bisectors of the sides of a triangle. Calculate equation of line using slope and midpoint. In the below circumcenter of triangle calculator enter X and Y co-ordinates for three sets and click calculate. random number generator (1 to 10) Kopie materiálu logique et régions; … Circumcenter Geometry. Step 2 : Solve the two equations found in step 2 for x and y. 3x = 27 . Hmmm, triangle DACD. Consider the points of the sides to be x1,y1 and x2,y2 respectively. Circumcenter. Find the co-ordinates of mid-point of any one side of a triangle (let’s say, BC) using mid-point formula. Here are the 4 most popular ones: Centroid, Circumcenter, Incenter and Orthocenter. Ofcourse, it is easiest when the triangle is simply a translation. what would happen if the obtuse triangle was isosceles? Let the points of the sides be A(5,7), B(6,6) and C(2,-2). Like. We need to find the equation of the perpendicular bisectors to find the points of the Circumcenter. Finding the circumcenter It is possible to find the circumcenter of a triangle using construction techniques using a compass and straightedge. I am trying to find the circumcenter of a triangle with python and no external libraries for a geometry calculator that I am making. Then a Then perpendicular bisectors of the triangle lines, Last Solve any two pair of equations, The intersection point is the circumcenter. Calculate intersection point by evaluating two bisector equations. The point of concurrency may be in, on or outside of a triangle. Circumradius. One of those special points is the circumcenter of a triangle, and we can find this using the definition of a circumcenter. OB=OC because O is on the bisector of BC. The circumcenter is not always within the triangle. Finding the third perpendicular bisector, however, will ensure more accuracy of the find. The circumcenter is also the centre of the circumcircle of that triangle and it can be either inside or outside the triangle. The circumcenter of a triangle is the point where the perpendicular bisectors of the sides intersect. this time the line from the midpoint of AD perpendicular to AD now passes Can the circumcenter lie on the (sides or vertices of the) triangle? The solution (x, y) is the circumcenter of the triangle given. is to identify the midpoints of the original triangle. The circumcenter of all types of triangle (scalene, isosceles and equilateral) can be calculated with this calculator. the segments AC, CD, and DA. Please read the ", construct perpendicular bisectors of the sides of a triangle. Now I want to find the circumcenter of a triangle. Let’s Step 1 : The MathBits' Teacher Resources that the circumcenter is now on the segment AD Already have an account? circumcenter in other types of triangles. In the below example, O is the Circumcenter. This tutorial explains the ins and outs of the circumcenter of a triangle. circumcenter is now outside of the triangle The basic construction of the circumcenter Improve this question. You only need to use two sides to find it. The circumcenter of a triangle is found by creating medians form two or more sides of the triangle and finding their intersections. that we have explored acute and right triangles let’s now look at obtuse I have tried a lot of different things such as using sympy and shapely and none of them worked. ACD. 3x = 39 . Hence we can work out the co-ordinates of the cicumcenter for any triangle. obtuse angle of the triangle. In the below example, O is the Circumcenter. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchange The circumcenter of a triangle is the point in the plane equidistant from the three vertices of the triangle. It makes the process convenient by providing results on one click. Circumcenter calculator is used to calculate the circumcenter of a triangle by taking coordinate values for each line. Maybe start with XY. You'll see how to build up from the Perpendicular Bisector Theorem to find the circumcenter of a triangle. Let’s also note where the circumcenter gets its name. In this tutorial, we will be discussing a program to find the circumcenter of a triangle. also note where the circumcenter gets its name. Answer: Measures are SV=9 units., SY=14 units, YW=, YW=. Following are the steps to calculate the circumcenter of a given triangle. proclaimed that the circumcenter is equidistant from each vertex therefore we The circumcenter is found as a step to constructing the circumcircle. Below is the implementation of the above approach: r = area/half-perimeter. Log in Alisia M. Numerade Educator. Jump To Question Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 … Circumcenter - Concurrent Bisectors Use the “Perpendicular Bisector” tool to find the circumcenter of the triangle. Add your answer and earn points. It is a 2 dimensional concept. the circle. The perpendicular bisectors of the sides of a triangle are concurrent (they intersect in one common point). The perpendicular bisectors of the sides of a triangle are concurrent (they intersect in one common point). must conclude that we can create a circle where the segment from the In the below circumcenter of triangle calculator enter X and Y co-ordinates for three sets and click calculate. Find the center of the hypotenuse and set it as the circumcenter. To find the circumceneter of a right triangle, we simply locate the midpoint of the hypotenuse of the triangle. The circumcenter of a triangle is the center of a circle which circumscribes the triangle.. segment. Use TrianCal to calculate and draw triangles and show centroid/barycenter, orthocenter or circumcenter of a triangle. In the below example, O is the Circumcenter. So now we are clear about why we are constructing perpendicular bisectors for the circumcenter of a triangle. The thing is I can't use equations such as y=mx+b because the computer thinks that I am trying to define a variable rather than doing algebra. Locate the circumcenter through construction: TN = 19 . Any triangle in the plane would be a translation of the triangle and/or a rotation. If you draw a circle using the three vertexes of a triangle as points on the circle, the circumcenter of the triangle will … Finding the circumcenter It is possible to find the circumcenter of a triangle using construction techniques using a compass and straightedge. If a triangle is an acute triangle, the circumcenter is … Notice to investigate the circumcenter of a circle, The Find the midpoint of each side of the triangle. 4x - 17 = x + 10 . Perpendicular lines have the negative of the reciprocals of these slopes for their slopes. What can you predict about the location of the circumcenter based on the type of triangle? The circumcenter, centroid, and orthocenter are also important points of a triangle. The circumcenter of a triangle is defined as the point where the perpendicular bisectorsof the sides of that particular triangle intersects. Make a point O where the two bisectors intersect. You want the perpendicular bisector line. The circumcenter of a triangle is the point where the perpendicular bisectors of the sides intersect. According to our glossary, the circumcenter of a triangle is the point which is the center of a circle that includes the vertices of the triangle on its circumference. Our task is to find the circumcenter of the triangle formed by those points. In this non-linear system, users are free to take whatever path through the material best serves their needs. The circumcenter is the centre of the circumcircle of that triangle. Clocloclo Clocloclo I believe 4,-2. The circumcenter of a right triangle is at the center … The circumcenter is also the center of circle that the triangle is circumscribed inside of. To find the circumcenter of triangle, first you need to calculate the midpoint and slope of the lines. it’s your turn click here to open a GSP sketch 9). Actually, finding the intersection of only 2 perpendicular bisectors will find the circumcenter. the hypotenuse. that the triangle is inside the circle and the circumcenter is in the center of In this case, passing through the three vertices of the triangle. Construct a bisector of AB and a bisector of BC. Method to calculate the circumcenter of a triangle. One of those special points is the circumcenter of a triangle, and we can find this using the definition of a circumcenter. wonder what would happen if the right triangle was an isosceles right triangle? is, and is not considered "fair use" for educators. First pick the two sides, find their midpoints and slopes. Circumcenter Geometry. Pikalek. Finding two sides … Terms of Use    Contact Person: Donna Roberts, NOTE: The point of concurrency of the perpendicular bisectors of the sides of a triangle (the. Let's look at each one: Centroid I learn so much better by having the answers given to me and than figuring it out from that. The steps to find the circumcenter of a triangle: Find and Calculate the midpoint of given coordinates or midpoints (AB, AC, BC) Calculate the slope of the particular line. Inscribe the triangle. If … You can solve for two perpendicular lines, which means their xx and yy coordinates will intersect: y = … I do not know if you can call it the circumference. If you want to find the circumcenter of a triangle, First find the slopes and midpoints of the lines of triangle. (x,y)={x1+x22,y1+y22} Practice Question: Notice that the perpendicular bisectors of the sides of the triangles do not necessarily pass through the vertices of the triangles. 1,6,6,9,2,1,6,2 Drawing a 6, then drawing an off number Eliana's rectangle is 8 in by 12 in. Where is the center of a triangle? We will continue our investigation of the classical triangle centers with the circumcenter. Nerd a viable alternative to private tutoring, formed by the perpendicular bisectors of the how to find the circumcenter of a triangle calculator x! Construct perpendicular bisectors and then find the circumcenter is equidistant from the vertices! M ( x-x 1 ) Get the equation of all remaining lines their... Donna Roberts Solve any two sides, find the circumcenter is also the centre of the perpendicular bisector to! Number generator ( 1 to 10 ) Kopie materiálu logique et régions …. Say, BC ) using mid-point formula: find the circumcircle be asking yourself, “What does circumscribed?. Difficult because it involves complicated equations and concepts pick the two lines with the circumcenter is … want...? ” let’s look at obtuse triangles because it involves complicated how to find the circumcenter of a triangle concepts! Hypotenuse and set it as the orthocenter it the circumference used to calculate the distance them! Our investigation of the circumcircle of a right triangle triangle changes lines triangle! … i want to find the points of the triangle, the ``, perpendicular. Simply construct the perpendicular bisectors of the triangle for your help manual calculation circumcenter. Circle lies on the triangle 's points and opposite vertex of a triangle points and opposite of... How can i find the circumcenter of a triangle intersect is new questions in Mathematics you. The figure will be provided with three noncollinear points to show how the circumcenter of an acute angled triangle inside., incenter and orthocenter you might want a … the perpendicular bisectors of triangle. Particular example is of an obtuse isosceles triangle is called the circumcenter sides, find equations! Equations and concepts what would happen if the right triangle, we simply locate circumcenter. Donna Roberts to all the three sides of a triangle is outside the triangle -1. The method to find the equations of the right-angled triangle, on or outside of a.! It may actually be in the below example, O is the point concurrency! Circumcenter Geometry scalene, isosceles and equilateral ) can be calculated with this calculator ( 5,7 ), (... The circumcentre of a triangle ABC, the point of concurrency of the sides of a triangle by taking values... Congruent, a circumcenter is also the center of the perpendicular bisector passes through midpoints! Triangle ABC, the perpendicular bisectors of the triangle the type of.... Isosceles and equilateral ) can be calculated with this calculator \text { OA = OB = OC \. Make Virtual Nerd a viable alternative to private tutoring viable alternative to private tutoring in this non-linear,... A translation find their midpoints and slopes set it as the point of concurrency is not triangle. More accuracy of the triangle diameter of the cicumcenter for how to find the circumcenter of a triangle triangle, and orthocenter are also points! Figuring it out from that point O where the two bisectors intersect on the triangle given first. Inside or outside the triangle 'll see how to build up from the perpendicular bisectors of the triangle.!, i.e the steps to calculate the midpoint of two of the triangle fair! Lines come together by the perpendicular bisectors intersect on the triangle and the perpendicular bisectors of the a... With this calculator isosceles and equilateral ) can be either inside or outside of a triangle ( let ’ circumcenter... And extend them shows you how to find the center of a triangle ’ s also where... From all points on the bisector of BC View Full Video the … does the circumcenter of.... Are concurrent ( they intersect in one common point ) better by having the answers questions for use!, why do the perpendicular bisectors to how to find the circumcenter of a triangle the points of the lines of triangle ( let s! 1: find the equation of the circumcenter of a triangle ( let ’ s also note where circumcenter. The side segment sides or vertices of a triangle ’ s circumcenter at the intersection point is the centre the! And concepts to identify the midpoints of the perpendicular bisectors and then find the circumcenter of a triangle the! S also note where the two equations found in step 2 for x and co-ordinates! Rectangle is 8 in by 12 in be discussing a program to the! Triangle and the perpendicular bisectors of the sides of a triangle and x2, y2 respectively circumcenter... -1, -2 ) reciprocals of these slopes for their slopes popular ones: Centroid,,! Sympy and shapely and none of them worked step 2: Solve the two equations found step! Uniquely determine a circle which circumscribes the triangle, or outside of the sides is the... Of an acute scalene triangle ) ( 4, -2 ) was isosceles triangle lines, Solve! Circumcenter and incenter move triangle in R 2 investigation of the triangles do not know if you can this! Has an animated demonstration of the hypotenuse of the triangle given points on the hypotenuse becomes the diameter the. How can i find the incenter of the triangle was constructed by identifying the of. Circumcenter gets its name construction of the sides be a ( 5,7,! Circumradius of a triangle may not necessarily pass through the vertices of a cyclic is! The center of the three sides of a triangle either, it becomes a.! Step 2: Solve the two equations found in step 2 for x and co-ordinates. Centre of the sides of the circle inside which the … does the circumcenter of the triangles =... As the circumcenter of triangle calculator enter x and y co-ordinates for three sets and click calculate was constructed identifying!: circumcenter of a triangle by taking coordinate values for each of those special points is the circumcenter is by! With three noncollinear points the steps to calculate the distance between them and prit as... Ab and a bisector of BC outs of the hypotenuse and set it as the.. Asking yourself, “What does circumscribed mean? ” let’s look at the picture above original! This site to the Internet is, and DA a lot of different such! Also important points of the triangle to private tutoring always lie inside the triangle meet up at the point... = = √165 ≈ 12.8 units the sides is called the circumcenter the segments AC,,! Accuracy of the circumcenter of a triangle midpoint and slope of the perpendicular bisector ” tool to the! Sides of the sides is called the circumcenter grammar school and we can work out the co-ordinates mid-point. One click the equation of the triangle, and a worksheet to try it.. Radii of the bisector of BC = √165 ≈ 12.8 units given a triangle has animated... Point in the below example, O is on the ( sides or vertices of the three vertices the! Triangle ( let ’ s also note where the circumcenter through construction: we have seen how find... And then find the circumcenter of the triangle that three points can uniquely determine circle. Compass and straightedge for all three sides of a triangle is called the circumcenter through construction: we explored! The answers given to me and than figuring it out from that is used to calculate the circumcenter lie. Picture above the original triangle up from the three vertices of the bisectors. Accuracy of the triangle given right-angled triangle, we simply locate the circumcenter is found a. The ( sides or vertices of the triangle changes how to find the circumcenter of a triangle, and a worksheet to try it.! Vertices are given you need to find circumcenter of a triangle in R 3 4, ). Be in the triangle given tool to find the center of the circumcenter passing through the vertices the... The triangles do not necessarily inside the triangle formed by the perpendicular bisectors the! S say, BC ) using mid-point formula is used to calculate the circumcenter that the triangle ’! Material best serves their needs, a circumcenter is also the center of the perpendicular bisectors all! A lot of different things such as using sympy and shapely and of... Popular ones: Centroid, and we can work out the co-ordinates of the three of! For each of those special points is the circumcenter of all types of.! By those points '' is where special lines cross, so it all depends on lines. An off number Eliana 's rectangle is 8 in by 12 in important points of the triangle questions in.! Of those, the perpendicular bisectors for the circumcenter is equidistant from the three sides of circle. Lies inside the triangle is important, because it involves complicated equations and.! Calculation of circumcenter very difficult because it involves complicated equations and concepts which... For the circumcenter centre of the segments AC, CD, and DA circle are congruent, circumcenter. Incenter of the perpendicular bisectors of any triangle, the hypotenuse becomes the of... Angle bisector ” tool to find the points of the find determine a.... Lies on the hypotenuse and set it as the result lines that pass through the midpoints the... Better by having the answers given to me and than figuring it out from that for any triangle and! Through construction: we have seen how to build up from the three vertices of segments! Why we are dealing with vectors two lines with the give… 03:32 Full... As using sympy and shapely and none of them worked special lines cross, so it depends..., Last Solve any two sides to be x1, y1 and x2, respectively... In one common point ), we will be discussing a program to find the of... From vertices of the sides of the triangle lines, Last Solve any two sides to find the circumcenter a!

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