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two circles and their common tangents

Source: All-Russian 2007

May 4, 2007

geometryparallelogramgeometry proposed

Problem Statement

Two circles

\omega_{1}

and

\omega_{2}

intersect in points

A

and

B

. Let

PQ

and

RS

be segments of common tangents to these circles (points

P

and

R

lie on

\omega_{1}

, points

Q

and

S

lie on

\omega_{2}

). It appears that

RB\parallel PQ

. Ray

RB

intersects

\omega_{2}

in a point

W\ne B

. Find

RB/BW

. S. Berlov

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