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Ratio in isosceles right triangle

Source: Serbian JBTST 2, Day 1

May 30, 2009
ratiotrigonometrygeometry proposedgeometry

Problem Statement

In isosceles right triangle ABC ABC a circle is inscribed. Let CD CD be the hypotenuse height (DāˆˆAB D\in AB), and let P P be the intersection of inscribed circle and height CD CD. In which ratio does the circle divide segment AP AP?
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