IMO 2007 Shortlist G7
Given an acute triangle ABC with angles α, β and γ at vertices A, B and C, respectively, such that β > γ. Point I is the...
Category: Geometry
Problem
Given an acute triangle ABC with angles α, β and γ at vertices A, B and C, respectively, such that β > γ. Point I is the incenter, and R is the circumradius. Point D is the foot of the altitude from vertex A. Point K lies on line AD such that AK = 2R, and D separates A and K. Finally, lines DI and KI meet sides AC and BC at E and F, respectively. Prove that if IE = IF then β ≤ 3γ. (Iran)