MathDB
Equal inradii

Source: Indian IMOTC 2013, Practice Test 2, Problem 2

May 10, 2013
trigonometryLaTeXgeometrygeometric transformationreflectiontrig identitiesLaw of Sines

Problem Statement

In a triangle ABCABC with B=90∘B = 90^\circ, DD is a point on the segment BCBC such that the inradii of triangles ABDABD and ADCADC are equal. If ADB^=φ\widehat{ADB} = \varphi then prove that tan⁡2(φ/2)=tan⁡(C/2)\tan^2 (\varphi/2) = \tan (C/2).
Back to ProblemsView on AoPS