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Centroamerican Olympiad 2010, problem 6

Source:

May 30, 2010

ratiogeometry proposedgeometry

Problem Statement

Let

\Gamma

and

\Gamma_1

be two circles internally tangent at

A

, with centers

O

and

O_1

and radii

r

and

r_1

, respectively (

r>r_1

).

B

is a point diametrically opposed to

A

in

\Gamma

, and

C

is a point on

\Gamma

such that

BC

is tangent to

\Gamma_1

at

P

. Let

A'

the midpoint of

BC

. Given that

O_1A'

is parallel to

AP

, find the ratio

r/r_1

.

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