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Incircle and length of segments

Source: ItaMO 2001 Problem 5

February 17, 2013
geometrygeometric transformationhomothetyincenter

Problem Statement

Let ABCABC be a triangle and γ\gamma the circle inscribed in ABCABC. The circle γ\gamma is tangent to side ABAB at the point TT. Let DD be the point of γ\gamma diametrically opposite to TT, and SS the intersection point of the line through CC and DD with side ABAB. Prove that AT=SBAT=SB.
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