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European Mathematical Cup 2016 junior division problem 2

Source:

December 31, 2016

geometryemc

Problem Statement

Two circles

C_{1}

and

C_{2}

intersect at points

A

and

B

. Let

P

,

Q

be points on circles

C_{1}

,

C_{2}

respectively, such that

|AP| = |AQ|

. The segment

PQ

intersects circles

C_{1}

and

C_{2}

in points

M

,

N

respectively. Let

C

be the center of the arc

BP

of

C_{1}

which does not contain point

A

and let

D

be the center of arc

AE

of

C_{2}

which does not contain point

A

Let

E

be the intersection of

CM

and

DN

. Prove that

AE

is perpendicular to

CD

.
Proposed by Steve Dinh

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