MathDB

Let

ABCD

be a non-isosceles trapezoid with

AB \parallel CD

. A circle through

A

and

B

meets

AD

BC

E, F

. The segments

AF, BE

meet at

G

. The circumcircles of

\triangle ADG

and

\triangle BCG

meet at

H

. Show that if

GD=GC

H

is the orthocenter of

\triangle ABG

2