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