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Chisinau MO p132 1976 X AB/CD = AO x BO / CO x DO in tangential ABCD

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March 16, 2021
geometryratiotangential

Problem Statement

Let OO be the center of a circle inscribed in a convex quadrilateral ABCDABCD and ∣AB∣=a|AB|= a, ∣CD∣=|CD|=c. Prove that ac=AO⋅BOCO⋅DO.\frac{a}{c}=\frac{AO\cdot BO}{CO\cdot DO}.
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