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1994 USAMO Problems/Problem 3

Revision as of 23:05, 22 May 2014 by Swamih (talk | contribs) (Created page with "==Problem== A convex hexagon <math>ABCDEF</math> is inscribed in a circle such that <math>AB=CD=EF</math> and diagonals <math>AD,BE</math>, and <math>CF</math> are concurrent. Le...")
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Problem

A convex hexagon $ABCDEF$ is inscribed in a circle such that $AB=CD=EF$ and diagonals $AD,BE$, and $CF$ are concurrent. Let $P$ be the intersection of $AD$ and $CE$. Prove that $\frac{CP}{CE}=(\frac{AC}{CE})^2$.

Solution

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