# Circumcircles of Two Midpoints and an Altitude

Circumcircles of Two Midpoints and an Altitude

In the triangle let and be the midpoints of the sides and and let be the foot of the altitude from to . Prove that the circumcircles of the triangles , , and have a common point and that the line passes through the midpoint of the segment .

ABC

B'

C'

AC

AB

H

A

BC

AB'C'

BC'H

B'CH

I

HI

B'C'