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Show that C lies on the line RS.

Source: Austrian Mathematical Olympiad 2003, Part 2, D2, P3

June 18, 2011
projective geometrygeometry unsolvedgeometry

Problem Statement

Let ABCABC be an acute-angled triangle. The circle kk with diameter ABAB intersects ACAC and BCBC again at PP and QQ, respectively. The tangents to kk at AA and QQ meet at RR, and the tangents at BB and PP meet at SS. Show that CC lies on the line RSRS.
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