# Finding an angle, given various angles and lengths

I've been slaving over this for a couple days now and I can't seem to get a resolution at all.
Can anyone solve for $\alpha$?

Given data is the length of the red line that isn't tangential, $\angle$ $\delta$, $\angle$L and The length of the radius of the circle.

-
What is the data given on this problem ? –  Belgi Sep 27 '12 at 0:54
The given data is $\partial$ and L. I probably shouldn't have used $\partial$ as a variable :S –  Korvin Szanto Sep 27 '12 at 0:57
So, the radius of the circle is not given? –  Gerry Myerson Sep 27 '12 at 1:05
I misspoke, Radius of the circle is given aswell, I've edited my question. –  Korvin Szanto Sep 27 '12 at 1:05

Since you have the lengths and directions of two sides of the triangle, you can compute the coordinates of its right-hand vertex relative to the centre of the circle; their ratio gives you $\tan\alpha$:
$$\alpha=\arctan\frac{r\sin\partial+d\sin(\partial-\pi+L)}{r\cos\partial+d\cos(\partial-\pi+L)}\;,$$
where $r$ is the radius and $d$ is the length of the red line.