For a cyclic quadrilateral, the sum of the products of the two pairs of opposite sides equals the product of the diagonals.

We have three colored segment in this animation. Surprisingly the length of the longest one is always the sum of the length of the two smaller ones.

This is actually a very special case of Ptolemy’s theorem. The theorem gives a connection between the sides and the diagonals of a cyclic quadrilateral. In this case the length of the dashed lines is equal so the theorem can be simplified to the statement above.

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