Finding the Circumcircles

Marianne Parsons


Given triangle ABC, find the circumcircle of triangle AHB, triangle BHC, and triangle CHA.

Remember, the circumcircle is defined as the circumscribed circle that passes through each of the triangle's vertices whose center is the circumcenter. The circumcenter can be found at the intersection of the triangle's perpendicular bisectors.


Triangle ABC

We can see the perpendicular bisectors of this triangle intersect at point O. Therefore, O is the circumcenter.

Triangle AHB

We can see the perpendicular bisectors of this triangle intersect at point d. Therefore, d is the circumcenter.

Triangle BHC

We can see the perpendicular bisectors of this triangle intersect at point e. Therefore, e is the circumcenter.

Triangle CHA

We can see the perpendicular bisectors of this triangle intersect at point f. Therefore, f is the circumcenter.

Return to Assignment 8