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Part of 2011 Rioplatense Mathematical Olympiad, Level 3

Problems(1)

parallelogram from intersections, starting with 2 intersecting circles

Source: Rioplatense Olympiad 2011 level 3 P4

9/3/2018
We consider Γ1\Gamma_1 and Γ2\Gamma_2 two circles that intersect at points PP and QQ . Let A,BA , B and CC be points on the circle Γ1\Gamma_1 and D,ED , E and FF points on the circle Γ2\Gamma_2 so that the lines AEA E and BDB D intersect at PP and the lines AFA F and CDC D intersect at QQ. Denote MM and NN the intersections of lines ABA B and DED E and of lines ACA C and DFD F , respectively. Show that AMDNA M D N is a parallelogram.
geometryparallelogramcircles