Problem 34.
Right Triangle, Incircles, Inradius. Level: High School, SAT
Prep, College geometry
The figure shows a right
triangle
ABC, r is the
inradius.
Point D is taken on side AC, the
incircles
of triangles ABC, ABD and BDC touches the sides at E, F,
G, H, J, K, L, M, and N, respectively. Prove that DN = GK = EH
and r = BJ - DL
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