IMO 1985 LL MON52

In the triangle ABC, let B1 be on AC, E on AB, G on BC,

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IMO 1985 LL MON52

Origin: MON

Problem

In the triangle ABC, let B1 be on AC, E on AB, G on BC, and let EG be parallel to AC. Furthermore, let EG be tangent to the inscribed circle of the triangle ABB1 and intersect BB1 at F. Let r, r1, and r2 be the inradii of the triangles ABC, ABB1, and BFG, respectively. Prove that r = r1 + r2.