Given a right triangle with legs \(a\) and \(b\), inradius \(r\), and circumradius \(R\):

$$\large (a-r) + (b-r) = 2 R \quad\to\quad a + b = 2 ( R + r )$$

*Motivated by this question on the Mathematics Stack Exchange.*

Trigono**graphy** Trig, if you will, the picture ...

Given a right triangle with legs \(a\) and \(b\), inradius \(r\), and circumradius \(R\):

$$\large (a-r) + (b-r) = 2 R \quad\to\quad a + b = 2 ( R + r )$$

*Motivated by this question on the Mathematics Stack Exchange.*