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Geometry

Source: Belarus IMO TST 1995 Day 1 P 2

November 28, 2015

geometrycirclestangent circlescommon tangents

Problem Statement

Circles

S,S_1,S_2

are given in a plane.

S_1

and

S_2

touch each other externally, and both touch

S

internally at

A_1

and

A_2

respectively. The common internal tangent to

S_1

and

S_2

meets

S

at

P

and

Q.

Let

B_1

and

B_2

be the intersections of

PA_1

and

PA_2

with

S_1

and

S_2

, respectively. Prove that

B_1B_2

is a common tangent to

S_1,S_2

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