IMO 2006 Shortlist G4
A point D is chosen on the side AC of a triangle ABC with ∠C < ∠A < 90◦ in such a way that BD = BA. The incircle of ABC ...
Category: Geometry
Problem
A point D is chosen on the side AC of a triangle ABC with ∠C < ∠A < 90◦ in such a way that BD = BA. The incircle of ABC is tangent to AB and AC at points K and L, respectively. Let J be the incentre of triangle BCD. Prove that the line KL intersects the line segment AJ at its midpoint. (Russia)