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Perpendicular diagonals and equality with sum of inradii.

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February 19, 2011
geometryperimeterinradiusgeometry proposed

Problem Statement

The diagonals of a convex quadrilateral ABCDABCD are perpendicular to each other and intersect at the point OO. The sum of the inradii of triangles AOBAOB and CODCOD is equal to the sum of the inradii of triangles BOCBOC and DOADOA. (a)(a) Prove that ABCDABCD has an incircle. (b)(b) Prove that ABCDABCD is symmetric about one of its diagonals.
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