Hello, therealdrag0!
I have the length of a chord, and I have the included angle.
How can I find the radius of the circle? Did you follow skeeter's suggestion?
Code:
* * * A
* *
* / | *
* r / | *
/ |
* / | *
* O * θ |d *
* \ | *
\ |
* r \ | *
* \ | *
* *
* * * B
You know: .$\displaystyle \begin{array}{ccc}d \:=\:\text{length of chord }AB \\
\theta \:=\: \text{in{c}luded angle }AOB \end{array}$
Law of Cosines: .$\displaystyle d^2 \:=\:r^2 + r^2 - 2r^2\cos\theta$
. . $\displaystyle d^2 \:=\: 2r^2 - 2r^2\cos\theta \:=\: 2r^2(1 - \cos\theta) \:=\:4r^2\left(\frac{1-\cos\theta}{2}\right) \quad\Rightarrow\quad d^2\:=\:4r^2\sin^2\!\left(\tfrac{\theta}{2}\right)$
Hence, we have: .$\displaystyle d \:=\:2r\sin\tfrac{\theta}{2} \quad\Rightarrow\quad r \:=\:\frac{d}{2\sin\frac{\theta}{2}} \quad\Rightarrow\quad r\;=\;\tfrac{1}{2}d\csc\tfrac{\theta}{2}$
There! . . . We just invented a formula for this problem . . .