MathDB
Find the ratio of radii

Source: INMO 1995 Problem 4

October 6, 2005
ratiogeometrytrigonometryincenterhomothetyangle bisectorINMO

Problem Statement

Let ABCABC be a triangle and a circle Γ′\Gamma' be drawn lying outside the triangle, touching its incircle Γ\Gamma externally, and also the two sides ABAB and ACAC. Show that the ratio of the radii of the circles Γ′\Gamma' and Γ\Gamma is equal to tan⁡2(π−A4).\tan^ 2 { \left( \dfrac{ \pi - A }{4} \right) }.
Back to ProblemsView on AoPS