Problem 32. Triangle, Cevian, Incircles. Level: High School, SAT Prep, College geometry

Point D is taken on side AC of triangle ABC, the incircle E of triangle ABC touches AC at H, the incircle F of triangle ABD touches BD at L, and the incircle G of triangle BDC touches BD at K. Prove that DH = KL.
A cevian (BD) is a line segment which joins a vertex of a triangle with a point on the opposite side (or its extension).