MathDB

Config geo with symmedian

Source: Serbia Additional IMO TST 2024, P3 (out of 4)

May 30, 2024

geometry

Problem Statement

Let

ABC

be a triangle with circumcenter

O

, angle bisector

AD

with

D \in BC

and altitude

AE

with

E \in BC

. The lines

AO

and

BC

meet at

I

. The circumcircle of

\triangle ADE

meets

AB, AC

at

F, G

and

FG

meets

BC

at

H

. The circumcircles of triangles

AHI

and

ABC

meet at

J

. Show that

AJ

is a symmedian in

\triangle ABC

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