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Geometric Inequality - South African Maths Olympiad

Source: SAMO Senior Round 3 2013 Problem 6

September 17, 2013
inequalitiesgeometrycircumcirclegeometry unsolved

Problem Statement

Let ABCABC be an acute-angled triangle with AC≠BCAC \neq BC, and let OO be the circumcentre and FF the foot of the altitude through CC. Furthermore, let XX and YY be the feet of the perpendiculars dropped from AA and BB respectively to (the extension of) COCO. The line FOFO intersects the circumcircle of FXYFXY a second time at PP. Prove that OP<OFOP<OF.
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