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3

Part of 1993 China National Olympiad

Problems(1)

China Mathematical Olympiad 1993 problem3

Source: China Mathematical Olympiad 1993 problem3

9/22/2013
Let K,K1K, K_1 be two circles with the same center and their radii equal to RR and R1(R1>R)R_1 (R_1>R) respectively. Quadrilateral ABCDABCD is inscribed in circle KK. Quadrilateral A1B1C1D1A_1B_1C_1D_1 is inscribed in circle K1K_1 where A1,B1,C1,D1A_1,B_1,C_1,D_1 lie on rays CD,DA,AB,BCCD,DA,AB,BC respectively. Show that SA1B1C1D1SABCD≥R12R2\dfrac{S_{A_1B_1C_1D_1}}{S_{ABCD}}\ge \dfrac{R^2_1}{R^2}.
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