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2006 USAMO Problems/Problem 6

Revision as of 19:57, 1 September 2006 by Boy Soprano II (talk | contribs) (standardized)

Problem

Let $\displaystyle ABCD$ be a quadrilateral, and let $\displaystyle  E$ and $\displaystyle F$ be points on sides $\displaystyle AD$ and $\displaystyle BC$, respectively, such that $\displaystyle AE/ED = BF/FC$. Ray $\displaystyle FE$ meets rays $\displaystyle BA$ and $\displaystyle CD$ at $\displaystyle S$ and $\displaystyle T$ respectively. Prove that the circumcircles of triangles $\displaystyle SAE, SBF, TCF,$ and $\displaystyle TDE$ pass through a common point.

Solution

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