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parallelogram wanted, intersecting circles and prependiculars given

Source: Balkan MO Shortlist 2013 G3 BMO

March 3, 2020
geometryparallelogramcirclesperpendicular

Problem Statement

Two circles Γ1\Gamma_1 and Γ2\Gamma_2 intersect at points M,NM,N. A line ℓ\ell is tangent to Γ1,Γ2\Gamma_1 ,\Gamma_2 at AA and BB, respectively. The lines passing through AA and BB and perpendicular to ℓ\ell intersects MNMN at CC and DD respectively. Prove that ABCDABCD is a parallelogram.
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