Given is a triangle ABC with incenter I and circumcircle ω. The incircle is tangent to BC at D. The perpendicular at I to AI meets AB,AC at E,F and the circle (AEF) meets ω and AI at G,H. The tangent at G to ω meets BC at J and AJ meets ω at K. Prove that (DJK) and (GIH) are tangent to each other. geometrymixtilinear incircle