How to find the coordinates of the mid point of the sector in a circle

Question

I have to find the coordinates of the mid point of the sector in the circumference of the circle . Could you please help ?

Let's consider the circle below with radius of 10cm with the center as (5,5) sector in Grey color is of 30degree.

Answer 1

Every point of the circle is given by the equations

$ x=x_c+r \cos \theta\\ y=y_c+r\sin\theta $

As I don't know how much is $\alpha$ you must do it by yourself. Suppose $\alpha=40°$. Then we have:

$x=5 +10\cos \left(\alpha+30°/2\right)=5+10\cos 55°\approx 10.74\\ y=5+10\sin \left(\alpha +30°/2\right)=5+10\sin 55°\approx 13.2 $

Hope this helps $$...$$