Question

In a cyclic quadrilateral show that the sum of the products of the opposite sides is equalto the productof the diagnals.
please help me

Answer 1

This is known as Ptolemy's Theorem

Here is a page with the proof

http://www.cut-the-knot.org/proofs/ptolemy.shtml

Answer 2

This proof may be useful, but it concerns the ratio of the diagonals, and the ratio of the sum of products of sides connected to the diagonals

http://www.cut-the-knot.org/triangle/InscribedQuadri.shtml

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Answer 3

Looks like Reiny found you the proof you want.