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Canadian Students Math Olympiad 2011 Problem 4

Source:

July 19, 2011

geometrygeometric transformationreflectionrotationdilationperpendicular bisectorgeometry proposed

Problem Statement

Circles

P

and

\Gamma_2

have centers

O_1

and

O_2

and intersect at

P

and

Q

. A line through

P

intersects

X

and

\Gamma_2

at

A

and

B

, respectively, such that

AB

is not perpendicular to

PQ

. Let

X

be the point on

PQ

such that

XA=XB

and let

Y

be the point within

AO_1 O_2 B

such that

AYO_1

and

BYO_2

are similar. Prove that

2\angle{O_1 AY}=\angle{AXB}

.
Author: Matthew Brennan

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