## 'Triangle Incircle Iteration' printed from http://nrich.maths.org/

If the angles in the first triangle are $a$, $b$ and $c$ prove that the angles in the second triangle are given (in degrees) by
$f(x) = (90 - x/2)$
where $x$ takes the values $a$, $b$ and $c$. Choose some triangles, investigate this iteration numerically and try to give reasons for what happens.