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Isosceles trapezoid

Source: Argentina MO 2009

November 10, 2009
geometrytrapezoidratiotrigonometrygeometry unsolved

Problem Statement

Isosceles trapezoid ABCD ABCD, with AB∥CD AB \parallel CD, is such that there exists a circle Γ \Gamma tangent to its four sides. Let T \equal{} \Gamma \cap BC, and P \equal{} \Gamma \cap AT (P≠T P \neq T). If \frac{AP}{AT} \equal{} \frac{2}{5}, compute ABCD \frac{AB}{CD}.
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