MathDB

In a triangle

ABC

, let

D

and

E

be the midpoints of

AB

and

AC

, respectively, and let

F

be the foot of the altitude through

A

. Show that the line

DE

, the angle bisector of

\angle ACB

and the circumcircle of

ACF

pass through a common point.
Alternate version: In a triangle

ABC

, let

D

and

E

be the midpoints of

AB

and

AC

, respectively. The line

DE

and the angle bisector of

\angle ACB

meet at

G

. Show that

\angle AGC

is a right angle.

Problem Statement