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romania tsts

Source: Romania TST for IMO 1994 second exam

September 6, 2017
triangle inequalitygeometryinequalities

Problem Statement

Let be given two concentric circles of radii RR and R1>RR_1 > R. Let quadrilateral ABCDABCD is inscribed in the smaller circle and let the rays CD,DA,AB,BCCD, DA, AB, BC meet the larger circle at A1,B1,C1,D1A_1, B_1, C_1, D_1 respectively. Prove that σ(A1B1C1D1)σ(ABCD)≥R12R2 \frac{\sigma(A_1B_1C_1D_1)}{\sigma(ABCD)} \geq \frac{R_1^2}{R^2} where σ(P)\sigma(P) denotes the area of a polygon P.P.
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