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IGO 2022 advanced/free P1

Source: Iranian Geometry Olympiad 2022 P1 Advanced, Free

December 13, 2022

geometry

Problem Statement

Four points

A

,

B

,

C

and

D

lie on a circle

\omega

such that

AB=BC=CD

. The tangent line to

\omega

at point

C

intersects the tangent line to

M

at

MA=ML

and the line

AD

at

K

and

L

. The circle

\omega

and the circumcircle of triangle

KLA

intersect again at

M

. Prove that

MA=ML

.
Proposed by Mahdi Etesamifard

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