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3 perpendicular bisectors and 6 concyclic points given, collinear wanted

Source: KJMO 2007 p4

April 30, 2019
geometryperpendicular bisectorConcycliccollinear

Problem Statement

Let PP be a point inside △ABC\triangle ABC. Let the perpendicular bisectors of PA,PB,PCPA,PB,PC be ℓ1,ℓ2,ℓ3\ell_1,\ell_2,\ell_3. Let D=ℓ1∩ℓ2D =\ell_1 \cap \ell_2 , E=ℓ2∩ℓ3E=\ell_2 \cap \ell_3, F=ℓ3∩ℓ1F=\ell_3 \cap \ell_1. If A,B,C,D,E,FA,B,C,D,E,F lie on a circle, prove that C,P,DC, P,D are collinear.
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