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Two lines meet at circle

Source: APMO 2008 problem 3

March 22, 2008

geometrycircumcircleAPMO

Problem Statement

Let

\Gamma

be the circumcircle of a triangle

ABC

. A circle passing through points

A

and

C

meets the sides

BC

and

BA

at

D

and

E

, respectively. The lines

AD

and

CE

meet

\Gamma

again at

G

and

H

, respectively. The tangent lines of

\Gamma

at

A

and

C

meet the line

DE

at

L

and

M

, respectively. Prove that the lines

LH

and

MG

meet at

\Gamma

.

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