Hansen's Theorem

For those of you not familiar with Hansen's Theorem, it is very useful when deriving the radii of the excircles of a right triangle. It states that the Sum of the squares of the radii of the three excircles of a right triangle, plus the square of the radius of its incircle is equal to the sum of the squares of the sides of the triangle.

The theorem also shows an elegant and quick method for calculating the radii of the 3 excircles of the triangle, and proves that the Sum of the 4 radii is equal to the Perimeter of the triangle.