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inradius of a tangential ABCD smaller than sum of inradii of ABC and ACD

Source: Sharygin Final 2007 9.1

April 30, 2019
geometryinradiusradiigeometric inequality

Problem Statement

Given a circumscribed quadrilateral ABCDABCD. Prove that its inradius is smaller than the sum of the inradii of triangles ABCABC and ACDACD.
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