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MMO 223 Moscow MO 1952 tangent incircles wanted when AB + CD = BC + AD

Source:

August 8, 2019
geometryincircletangent circles

Problem Statement

In a convex quadrilateral ABCDABCD, let AB+CD=BC+ADAB + CD = BC + AD. Prove that the circle inscribed in ABCABC is tangent to the circle inscribed in ACDACD.