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2020 IGO Elementary P2

Source: 7th Iranian Geometry Olympiad (Elementary) P2

November 4, 2020

geometryparallelogramangle bisector

Problem Statement

A parallelogram

ABCD

is given (

AB \neq BC

). Points

E

and

G

are chosen on the line

\overline{CD}

such that

\overline{AC}

is the angle bisector of both angles

\angle EAD

and

\angle BAG

. The line

\overline{BC}

intersects

\overline{AE}

and

\overline{AG}

at

F

and

H

, respectively. Prove that the line

\overline{FG}

passes through the midpoint of

HE

. Proposed by Mahdi Etesamifard

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