IMO 1992 LL THA70

Let two circles A and B with unequal radii r and R, respec-

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IMO 1992 LL THA70

Origin: THA

Problem

Let two circles A and B with unequal radii r and R, respec- tively, be tangent internally at the point A0. If there exists a sequence of distinct circles (Cn) such that each circle is tangent to both A and B, and each circle Cn+1 touches circle Cn at the point An, prove that \infty  n=1 |An+1An| < 4\piRr R + r .