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exists a cricle

Source: 2-nd Taiwanese Mathematical Olympiad 1993

January 14, 2007
geometryparallelogramsymmetrypower of a pointradical axisgeometry unsolved

Problem Statement

Let EE and FF are distinct points on the diagonal ACAC of a parallelogram ABCDABCD . Prove that , if there exists a cricle through E,FE,F tangent to rays BA,BCBA,BC then there also exists a cricle through E,FE,F tangent to rays DA,DCDA,DC.
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