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Determine the ratio

Source: Sharygin contest 2008. The correspondence round. Problem 19

September 3, 2008
ratiogeometryparallelogramgeometry proposed

Problem Statement

(V.Protasov, 10-11) Given parallelogram ABCD ABCD such that AB \equal{} a, AD \equal{} b. The first circle has its center at vertex A A and passes through D D, and the second circle has its center at C C and passes through D D. A circle with center B B meets the first circle at points M1 M_1, N1 N_1, and the second circle at points M2 M_2, N2 N_2. Determine the ratio M1N1/M2N2 M_1N_1/M_2N_2.
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