I've been struggling with this for quite some time now, anyone could help me perhaps with this?
Given an angle of an arbitrary degrees, and a circle with radius r. And imagine I would try to push the circle into the angle, touching the two lines of the angle.
What would be the position of the center point of the circle.
On
This is the derivation:
Given $r = \frac {\sin\frac\theta2}{1+\sin\frac\theta2}R$ where $R$ is the distance from vertex to furthest point on circle (this equation is given in this post.):
$$\text{Distance} = R-r$$
$$\text{Distance} = \frac {1+\sin\frac\theta2}{\sin\frac\theta2}r-r$$
To determine the point of tangency $A$, note that $r=OA\cdot\tan\alpha/2$ where $O$ is the origin (vertex of the angle).