MathDB

3 Circles

Source: NZMO 2

October 6, 2021

geometry

Problem Statement

Let

AB

be a chord of circle

\Gamma

. Let

O

be the centre of a circle which is tangent to

AB

at

C

and internally tangent to

\Gamma

at

P

. Point

C

lies between

A

and

B

. Let the circumcircle of triangle

POC

intersect

\Gamma

at distinct points

P

and

Q

. Prove that

\angle{AQP}=\angle{CQB}

.

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