MathDB

Chords

AA^{\prime}

BB^{\prime}

CC^{\prime}

of a sphere meet at an interior point

P

but are not contained in a plane. The sphere through

A

B

C

P

is tangent to the sphere through

A^{\prime}

B^{\prime}

C^{\prime}

P

. Prove that

\, AA' = BB' = CC'

Problem Statement