Editing Right triangle (section)

===Inradius and circumradius===
The radius of the [[incircle]] of a right triangle with legs <math>a</math> and <math>b</math> and hypotenuse <math>c</math> is
:<math>r = \frac{a+b-c}{2} = \frac{ab}{a+b+c}.</math>

The radius of the [[circumcircle]] is half the length of the hypotenuse,
:<math>R = \frac{c}{2}.</math>

Thus the sum of the circumradius and the inradius is half the sum of the legs:<ref name="Crux">''Inequalities proposed in "[[Crux Mathematicorum]]"'', [http://www.imomath.com/othercomp/Journ/ineq.pdf].</ref>

:<math>R+r = \frac{a+b}{2}.</math>

One of the legs can be expressed in terms of the inradius and the other leg as
:<math>a=\frac{2r(b-r)}{b-2r}.</math>