Ptolemy's Theorem. Level: High School, SAT Prep, College geometry

Let a cyclic quadrilateral ABCD. Then the sum of the products of the two pairs of opposite sides equals the product of its two diagonals. In other words the rectangle contained by the diagonals of any cyclic quadrilateral ABCD is equal to the sum of the rectangles contained by the pairs of opposite sides.

 


An interesting particular case is when ABCD is a rectangle, since we get another proof of Pythagoras' theorem.

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Last updated: February 14, 2007