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AD/DI_a - Iran NMO 2004 (Second Round) - Problem1

Source:

September 24, 2010
geometrytrigonometryLaTeXgeometry proposed

Problem Statement

ABCABC is a triangle and ∠A=90∘\angle A=90^{\circ}. Let DD be the meet point of the interior bisector of ∠A\angle A and BCBC. And let IaI_a be the A−A-excenter of △ABC\triangle ABC. Prove that: ADDIa≤2−1.\frac{AD}{DI_a}\leq\sqrt{2}-1.
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