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China Mathematical Olympiad 1988 problem2

Source: China Mathematical Olympiad 1988 problem2

November 4, 2013
geometryperimetergeometry unsolved

Problem Statement

Given two circles C1,C2C_1,C_2 with common center, the radius of C2C_2 is twice the radius of C1C_1. Quadrilateral A1A2A3A4A_1A_2A_3A_4 is inscribed in C1C_1. The extension of A4A1A_4A_1 meets C2C_2 at B1B_1; the extension of A1A2A_1A_2 meets C2C_2 at B2B_2; the extension of A2A3A_2A_3 meets C2C_2 at B3B_3; the extension of A3A4A_3A_4 meets C2C_2 at B4B_4. Prove that P(B1B2B3B4)≥2P(A1A2A3A4)P(B_1B_2B_3B_4)\ge 2P(A_1A_2A_3A_4), and in what case the equality holds? (P(X)P(X) denotes the perimeter of quadrilateral XX)
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