Magical Quadrilateral!

Geometry Level 5

A quadrilateral A B C D ABCD in which A B = a , B C = b , C D = c , D A = d AB=a, BC=b, CD=c, DA=d such that one circle can be inscribed in it and another circle can be circumscribed about it. Then compute cos ⁡ A \cos A .

a d + b c a d − b c \cfrac { ad+bc }{ ad-bc } a c − b d a c + b d \cfrac { ac-bd }{ ac+bd } a c + b d a c − b d \cfrac { ac+bd }{ ac-bd } a d − b c a d + b c \cfrac { ad-bc }{ ad+bc }

Sahil Bansal by Sahil Bansal , 21, India

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