Let M be the incenter of the tangential quadrilateral A₁A₂A₃A₄. Let line g₁ through A₁ be perpendicular to A₁M; define g₂,g₃ and g₄ similarly. The lines g₁,g₂,g₃ and g₄ define another quadrilateral B₁B₂B₃B₄ having B₁ be the intersection of g₁ and g₂; similarly B₂,B₃ and B₄ are intersections of g₂ and g₃, g₃ and g₄, resp. g₄ and g₁. Prove that the diagonals of quadrilateral B₁B₂B₃B₄ intersect in point M.

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