Geometry Problem 35 with Solution: Incenters and Inradii in Cyclic Quadrilatera, Diagonals, Rectangle

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The figure shows a cyclic quadrilateral ABCD. E, F, G, and H are the incenters and r_a, r_b, r_c, and r_d are the inradii of the triangles ABD, ABC, BCD and ACD respectively. Prove that EFGH is a rectangle and r_a + r_c = r_b + r_d.
 

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Last updated: Sep 19, 2014

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