Right angled triangles have 3 excircles, I'm struggling to find a formula which gives me the radius of all three excircles, I've been struggling with this for a while. I've done some googling and I think I have parts of the correct formula,
$$A = \sqrt(s*(s-a)*(s-b)*(s-c))$$
$A$ is the area of the right angled triangle. $a, b$ and $c$ are sides of the right angled triangle. $s$ is the semi-perimeter of the right angled triangle. $r_1, r_2$ and $r_3$ are the radius of the excircles.
Can anyone find the formula?
Preferably I would like a formula without using any angles
Thanks in advance