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In the figure below, the circles A,B,C,D are tangent to the circle O; a, b, c, d, x, y are the common tangent to circles A and B, B and C, C and D, D and A, A and C, and B and D respectively. Prove the generalized Ptolemy's theorem: x.y = a.c + b.d

See also:

Ptolemy's Theorem.

Cyclic Quadrilateral: Ratio of the Diagonals

Brahmagupta's Theorem Cyclic quadrilateral.

Quadrilaterals.

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