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1992 USAMO Problems/Problem 3

Revision as of 20:37, 22 February 2008 by ZzZzZzZzZzZz (talk | contribs) (New page: ==Problem== Chords <math>AA'</math>, <math>BB'</math>, and <math>CC'</math> of a sphere meet at an interior point <math>P</math> but are not contained in the same plane. The sphere throug...)
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Problem

Chords $AA'$, $BB'$, and $CC'$ of a sphere meet at an interior point $P$ but are not contained in the same plane. The sphere through $A$, $B$, $C$, and $P$ is tangent to the sphere through $A'$, $B'$, $C'$, and $P$. Prove that $AA'=BB'=CC'$.

Solution

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