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Easy Geometry in 2024 IMOC

Source: 2024 imocsl G1 (Night 2-G)

August 8, 2024

geometryIMOC

Problem Statement

Given quadrilateral

ABCD

.

AC

and

BD

meets at

E

, and

M, N

are the midpoints of

AC, BD

, respectively. Let the circumcircles of

ABE

and

CDE

meets again at

X\neq E

. Prove that

E, M, N, X

are concyclic.
Proposed by chengbilly

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