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A bound on a Ratio of Areas

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October 21, 2010
ratiogeometrycyclic quadrilateralgeometry unsolved

Problem Statement

Let γ,Γ\gamma,\Gamma be two concentric circles with radii r,Rr,R with r<Rr<R. Let ABCDABCD be a cyclic quadrilateral inscribed in γ\gamma. If AB→\overrightarrow{AB} denotes the Ray starting from AA and extending indefinitely in B′sB's direction then Let AB→,BC→,CD→,DA→\overrightarrow{AB}, \overrightarrow{BC}, \overrightarrow{CD} , \overrightarrow{DA} meet Γ\Gamma at the points C1,D1,A1,B1C_1,D_1,A_1,B_1 respectively. Prove that [A1B1C1D1][ABCD]≥R2r2\frac{[A_1B_1C_1D_1]}{[ABCD]} \ge \frac{R^2}{r^2} where [.][.] denotes area.
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