Circumcenter of a triangle is the point of intersection of all the three perpendicular bisectors of the triangle.
The circumcenter of a triangle can be found as the intersection of any two of the three perpendicular bisectors. Perpendicular bisectors are nothing but the line or a ray which cuts another line segment into two equal parts at 90 degree.
The circumcenter's position depends on the type of triangle:
- the circumcenter lies inside the triangle (acute angle)
- the circumcenter lies outside the triangle (obtuse angle)
- the circumcenter lies at the center of the hypotenuse (right angle)
Examples:
Calculate the midpoint of the sides AB, BC and CA which is the average of the x and y co-ordinates. Midpoint of a line in the triangle = x1+x2/2, y1+y2/2
Midpoint of AB = 5+6/2, 7+6/2 = (11/2, 13/2) Midpoint of BC = 6+2/2, 6-2/2 = (4, 2) Midpoint of CA = 2+5/2, -2+7/2 = (7/2, 5/2)