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ABCD cyclic --> incenters of BCD, etc. form rectangle

Source: Kedlaya; also: APMO 1996, Problem 3

January 23, 2005
geometryincenterrectanglecyclic quadrilateralgeometry proposedAngle Chasing

Problem Statement

If ABCDABCD is a cyclic quadrilateral, then prove that the incenters of the triangles ABCABC, BCDBCD, CDACDA, DABDAB are the vertices of a rectangle.
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