MathDB

SMO 2014

Source:

May 22, 2015

geometry

Problem Statement

On sides

BC

and

AC

of

\triangle ABC

given are

D

and

E

, respectively. Let

F

(

F \neq C

) be a point of intersection of circumcircle of

\triangle CED

and line that is parallel to

AB

and passing through C. Let

G

be a point of intersection of line

FD

and side

AB

, and let

H

be on line

AB

such that

\angle HDA = \angle GEB

and

H-A-B

. If

DG=EH

, prove that point of intersection of

AD

and

BE

lie on angle bisector of

\angle ACB

.
Proposed by Milos Milosavljevic

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