Problem

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

Tags: geometry, ratio, geometric transformation, Spiral Similarity



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