Problem

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

Tags: trigonometry, LaTeX, geometry, geometric transformation, reflection, trig identities, Law of Sines



In a triangle $ABC$ with $B = 90^\circ$, $D$ is a point on the segment $BC$ such that the inradii of triangles $ABD$ and $ADC$ are equal. If $\widehat{ADB} = \varphi$ then prove that $\tan^2 (\varphi/2) = \tan (C/2)$.