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).
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