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paralellogram and 2 circles given. equal segments wanted

Source: Sharygin 2006 finals 8.3

September 10, 2019
geometryparallelogramcirclesequal segments

Problem Statement

A parallelogram ABCDABCD is given. Two circles with centers at the vertices AA and CC pass through BB. The straight line ℓ\ell that passes through BB and crosses the circles at second time at points X,YX, Y respectively. Prove that DX=DYDX = DY.
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