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.

