What is the relationship between the width, height, and radius of an arc? What is the relationship between the width ($w$), height ($h$), and radius ($r$) of an arc?
Specifically, the relationship in terms of $h$.
I know this is a simple question - I'm a hobbyist engineer, and I'm having one of those moments, where your mind goes blank and you can't remember the simplest thing.



$w^2+(r-h)^2=r^2$
$w^2+r^2-2hr+h^2=r^2$
$h^2-2hr+w^2=0$
Quadratic in $h$.
Solution:
$h=\frac{2r\pm\sqrt{4r^2-4w^2}}{2}$
The positive case is rejected, leaving us with:
$h=\frac{2r-\sqrt{4r^2-4w^2}}{2}$
$h=r-\sqrt{r^2-w^2}$
The proof that the positive case is rejected is left to the reader as an exercise.
