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Prove that r1+r2=r (ILL 1985)

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September 13, 2010
geometrygeometry proposed

Problem Statement

In the triangle ABCABC, let B1B_1 be on AC,EAC, E on AB,GAB, G on BCBC, and let EGEG be parallel to ACAC. Furthermore, let EGEG be tangent to the inscribed circle of the triangle ABB1ABB_1 and intersect BB1BB_1 at FF. Let r,r1r, r_1, and r2r_2 be the inradii of the triangles ABC,ABB1ABC, ABB_1, and BFGBFG, respectively. Prove that r=r1+r2.r = r_1 + r_2.
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