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

Question

I&#039;m not great at mathematics so I&#039;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

Charlee Gentry · Accepted Answer

Assume the sector angle is   2  θ 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   θ from the   x axis. Then   O  =  (  r  cos  ⁡  θ  ,  r  sin  ⁡  θ  ) where   r  sin  ⁡  θ  =  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.