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Prove that there is a fixed point P

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October 31, 2010
geometrycircumcirclegeometry unsolved

Problem Statement

Let AA and BB be two fixed points in the plane. Consider all possible convex quadrilaterals ABCDABCD with AB=BC,AD=DCAB = BC, AD = DC, and ∠ADC=90∘\angle ADC = 90^\circ. Prove that there is a fixed point PP such that, for every such quadrilateral ABCDABCD on the same side of ABAB, the line DCDC passes through P.P.
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