Question

How do you find the coordinates of the circumcenter of a triangle?

Answer 1

The circumcenter is where the perpendicular bisectors of a triangle meet. It's inside for an acute, outside for an obtuse, and at the center of the hypotenuse for right triangles.

So first find the midpoints & slopes of the sides of the triangle, and find the slope of the perpendicular bisectors by taking the negative reciprocal of the slopes. Then with that, you can find the equations of the perpendicular bisectors.

(You really only need 2 since you can find the coordinates by solving any 2 of the 3 equations.)

Answer 2

@jacquelyn1237 thanks for the great answer, that was really helpful!!