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Prove that S(ABC)=AD^2 - ILL 1990 SWE1

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September 19, 2010
geometrygeometry unsolved

Problem Statement

Point DD is on the hypotenuse BCBC of right-angled triangle ABCABC. The inradii of triangles ADBADB and ADCADC are equal. Prove that SABC=AD2S_{ABC} = AD^2, where SS is the area function.
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