The questions from geometry are most fascinating to me. As a parent I love to learn geometry and shapes from my son's textbook. I came across this statement about the in-circle:
Let $m, n$ that are integers and $m > n$. Let $a = 2mn$, $b = m^2 - n^2$ and $c = m^2 + n^2$ be the sides of the Pythagorean triangle. Then the radius of the in-circle $r$ will be $nm - n^2$.
How can this happen?
Thanks in advance.