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Geometric Inequality with Excircle

Source: Turkey National Mathematical Olympiad 2018

December 2, 2018
geometric inequalitygeometryinequalitiesgeometry proposed

Problem Statement

In a triangle ABCABC, the bisector of the angle AA intersects the excircle that is tangential to side [BC][BC] at two points DD and EE such that D∈[AE]D\in [AE]. Prove that, ∣AD∣∣AE∣≤∣BC∣2∣DE∣2. \frac{|AD|}{|AE|}\leq \frac{|BC|^2}{|DE|^2}.
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