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Tangents to the circumcircle of ABC

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January 16, 2011
geometrycircumcirclegeometry proposed

Problem Statement

The tangents at AA and BB to the circumcircle of the acute triangle ABCABC intersect the tangent at CC at the points DD and EE, respectively. The line AEAE intersects BCBC at PP and the line BDBD intersects ACAC at RR. Let QQ and SS be the midpoints of the segments APAP and BRBR respectively. Prove that ∠ABQ=∠BAS\angle ABQ=\angle BAS.
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