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Two circles with centers

S_{1}

and

S_{2}

are externally tangent at point

K

. These circles are also internally tangent to circle

S

at points

A_{1}

and

A_{2}

, respectively. Denote by

P

one of the intersection points of

S

and common tangent to

S_{1}

and

S_{2}

K

.Line

PA_{1}

intersects

S_{1}

B_{1}

while

PA_{2}

intersects

S_{2}

B_{2}

. Prove that

B_{1}B_{2}

is common tangent of circles

S_{1}

and

S_{2}

Problem Statement