# The geometric mean of two numbers a and b is, by definition, square root(ab). Prove that the length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments into which the altitude partitions the hypotenuse.

Question

The geometric mean of two numbers a and b is, by definition, square root(ab). Prove that the length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments into which the altitude partitions the hypotenuse.