MathDB
nice problem(due hard)

Source: iranian second round (2002)

May 10, 2005
geometrycircumcircleparallelogramgeometry solved

Problem Statement

In a convex quadrilateral ABCDABCD with ∠ABC=∠ADC=135∘\angle ABC = \angle ADC = 135^\circ, points MM and NN are taken on the rays ABAB and ADAD respectively such that ∠MCD=∠NCB=90∘\angle MCD = \angle NCB = 90^\circ. The circumcircles of triangles AMNAMN and ABDABD intersect at AA and KK. Prove that AK⊥KC.AK \perp KC.
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