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Here is a proof using analytic tools, complex numbers, and formulas for the involved points in terms of them. Points in the plane will be denoted by capital letters like $A,B,C,D;N;P,Q,R,S$ and the corresponding affixes will be their lower cousins, respectively $a,b,c,d;n;p,q,r,s\in\Bbb C$, and decorations (sub- or upper indices) will be kept. First let us ...

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