Apollonius's theorem

This article is about the lengths of the sides of a triangle. For his work on circles, see Problem of Apollonius.
green/blue areas = red area
Pythagoras as a special case:
green area = red area

In geometry, Apollonius's theorem is a theorem relating the length of a median of a triangle to the lengths of its sides. It states that the sum of the squares of any two sides of any triangle equals twice the square on half the third side, together with twice the square on the median bisecting the third side. The theorem is named for the ancient Greek mathematician Apollonius of Perga.