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If ` vec a , vec b , vec ca n d vec d` are the position vectors of the vertices of a cyclic quadrilateral `A B C D ,` prove that `(| vec axx vec b+ vec bxx vec d+ vec d xx vec a|)/(( vec b- vec a)dot( vec d- vec a))+(| vec bxx vec c+ vec cxx vec d+ vec d xx vec b|)/(( vec b- vec c)dot( vec d- vec c))=0dot`

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