WOLFRAM|DEMONSTRATIONS PROJECT

Circumcircles of Two Midpoints and an Altitude

labels

In the triangle

ABC

let

B'

and

C'

be the midpoints of the sides

AC

and

AB

and let

H

be the foot of the altitude from

A

to

BC

. Prove that the circumcircles of the triangles

AB'C'

,

BC'H

, and

B'CH

have a common point

I

and that the line

HI

passes through the midpoint of the segment

B'C'

.