Finding the incircle of a circle sector I'm not great at mathematics so I'm sure this is trivial to most. I have been searching around however and not been able to find how to figure out the incircle of a circle sector, or, in other words, the point inside a sector that is furthest away from the radii and the arc. The simpler solution the better :) Thanks in advance.

Assume the sector angle is $2 \theta$ and the radius is $1$, with center at $(0,0)$ and one end of the arc at $(1,0)$. Then the angle bisector of the sector, on which the center $O$ of the incircle must lie, is at angle $\theta$ from the $x$ axis. Then $O=(r \cos \theta, r \sin \theta)$ where $r \sin \theta=1-r.$ Then $r$ may be found from this. Of course the whole diagram may have to be rescaled and rotated depending on how your sector is situated.