As we can see, all of our sides have perpendicular bisectors and all three of our bisectors meet at a point. 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Circumcenter calculator takes values from you as input and gives you accurate results in a few seconds. The point of concurrency may be in, on or outside of a triangle. Find the vertex opposite to the longest side and set it as the orthocenter. Calculate the distance between them and prit it as the result. the hypotenuse. So, the midpoint of side AB = (1 + 3 2, 2 + 6 2) = (2, 4) And slope of AB = 6 − 2 3 − 1 = 2 The slope of the perpendicular bisector = -1/slope of the line, Slope of the perpendicular bisector of AB = −1(3/2)=−23\dfrac{-1}{(3/2)} = \dfrac{-2}{3}(3/2)−1​=3−2​, Slope of the perpendicular bisector of BC = −1(10/3)=−310\dfrac{-1}{(10/3)} = \dfrac{-3}{10}(10/3)−1​=10−3​, Slope of the perpendicular bisector of CA = −17\dfrac{-1}{7}7−1​. All three perpendicular bisectors of the sides of a triangle will intersect at the same point - the circumcenter. Midpoint = (x1+x2)2\dfrac{(x1+x2)}{2}2(x1+x2)​ and (y1+y2)2\dfrac{(y1+y2)}{2}2(y1+y2)​. Next you need to find the intersection point by solving any two of the equations. You can use any calculator for free without any limits. The circumcenter of a triangle is defined as the point where the perpendicular bisectors of the sides of that particular triangle intersect. Fill the calculator form and click on Calculate button to get result here. Need to calculate the area of the triangle before calculating the circumcenter? In other words, the point of concurrency of the bisector of the sides of a triangle is called the circumcenter. Follow the below steps to find circumcenter of a triangle: Step 1: First of all, calculate the midpoint of the combined x and y coordinates of the sides AB, BC, and CA. Let us take (X, Y) be the coordinates of the circumcenter. Inscribe the triangle. See Construction of the Circumcircle of a Triangle has an animated demonstration of the technique, and a worksheet to try it yourself. How to find the circumcenter of a triangle. 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