MathDB

6

Part of 2006 USAMO

Problems(1)

Darij is going to solve Feng's Geometry Problem - Pwn it!

Source: USAMO 2006, Problem 6, proposed by Zuming Feng

4/20/2006
Let ABCDABCD be a quadrilateral, and let EE and FF be points on sides ADAD and BCBC, respectively, such that AEED=BFFC\frac{AE}{ED} = \frac{BF}{FC}. Ray FEFE meets rays BABA and CDCD at SS and TT, respectively. Prove that the circumcircles of triangles SAESAE, SBFSBF, TCFTCF, and TDETDE pass through a common point.
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