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Parallel tangets

Source:

May 27, 2006

geometrypower of a pointradical axisgeometry unsolved

Problem Statement

The circles

\gamma_1

and

\gamma_2

intersect at the points

\gamma

and

PA_1

and internally touch a circle

\gamma

at

A_1

and

A_2

respectively. Let

P

be an arbitrary point on

\gamma

. Segments

PA_1

and

PA_2

meet

\gamma_1

and

\gamma_2

again at

B_1

and

B_2

respectively. a) Prove that the tangent to

\gamma_{1}

at

B_{1}

and the tangent to

\gamma_{2}

at

B_{2}

are parallel. b) Prove that

B_{1}B_{2}

is the common tangent to

\gamma_{1}

and

\gamma_{2}

iff

P

lies on

QR

.

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