Geometry Problem 27: Right triangle, Altitude, Incenters, Inradius, Perpendicular Lines, 45 Degrees.

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In triangle ABC, angle B is a right angle. O is the incenter of triangle ABC, From O parallels FG and HM are drawn to AB, and BC. r1, and r2, are the inradii of the triangles AHM, and FGC respectively, the points D and E are points of tangency. Prove that . See also: Artwork of Problem 27.
 

Flyer of problem 27 using iPad Apps