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III Lusophon Mathematical Olympiad 2013 - Problem 2

Source:

August 12, 2013
geometrycircumcircletrigonometryperpendicular bisector

Problem Statement

Let ABCABC be an acute triangle. The circumference with diameter ABAB intersects sides ACAC and BCBC at EE and FF respectively. The tangent lines to the circumference at the points EE and FF meet at PP. Show that PP belongs to the altitude from CC of triangle ABCABC.
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