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).
Mind Map: George Pólya's 1945 book,
"How to Solve It"
George Pólya's 1945 book "How to Solve It, A new aspect of
Mathematical Method", is a book describing methods of problem
solving. It suggests the following steps when solving a
mathematical problem: (1) First, you have to understand the
problem. (2) After understanding, then make a plan. (3) Carry
out the plan. (4) Look back on your work. How could it be
better?
A mind map is a diagram used to visually organize information, knowledge, concepts or ideas.
