[Math] Calculate angle between a chord and the circle’s origin

Question

I need to make an arc that has a varied size. For that I need to calculate the starting and ending angle of the chord cutting the arc. How can I do that knowing only the radius and the chord's length.

How do I calculate $\alpha$ and $\beta$?

Answer 1

This is right triangle trig if you drop a perpendicular bisector from the chord to the circle center.

$\beta = 2\cdot \sin^{-1}(\frac{l}{2r})$

and $\alpha = \frac{180 - \beta}{2}$