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Two intersecting circles

Source: Pre-VMO 2012 - Problem 3

November 27, 2011

geometryincenterangle bisectorgeometry proposed

Problem Statement

Two circles

(O)

and

(O')

intersect at

A

and

B

. Take two points

P,Q

on

(O)

and

(O')

, respectively, such that

AP=AQ

. The line

PQ

intersects

(O)

and

(O')

respectively at

M,N

. Let

E,F

respectively be the centers of the two arcs

BP

and

BQ

(which don't contains

A

). Prove that

MNEF

is a cyclic quadrilateral.

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