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Conditional trapezoid geometry

Source: Silk Road 2024 P2

October 20, 2024

geometry

Problem Statement

Let

ABCD

be a non-isosceles trapezoid with

AB \parallel CD

. A circle through

A

and

B

meets

AD

,

BC

at

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

.

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