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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}.
See solution below
