Imagine the right-angled $\triangle ABC$ with an right angle at $C$ and side-lengths $|AB|= c$, $|BC|=a$, $|CA|=b$. Let $r$ be the radius of the inscribed circle. Then it follows that...
- (a) $r = \frac12(a + b − c)$
- (b) $r = \frac12(c − a − b)$
- (c) $r = \frac12(3a + 2b − 2c)$
- (d) $r = \frac12(2c − a − b)$
Why is alternative (a) correct? I can yet not fathom the reasoning behind it.