How to inscribe a circle in a circular sector?
First we have to have a sector with three points - A, B and C. The circle must be in the middle of the sector so we make a bisector from angle CAB. It intersects the circle in point D. Then we make a tangent to the original circle through point D. We extend the segment AC to be a half line so that it intersects the tangent in point E. We then make another bisector from angle AED. It intersects the other bisector in point F which is the center for out inscribed circle. All we have to do is make a circle from point F with radius of segment FD.