Sector is the area of a circle bounded by two radii and the corresponding arc.
In case if semi-circle one can draw a circle with the radius of the circle perpendicular to the diameter as diameter.
In case of major sector draw a diameter in the sector and draw the circle as drawn earlier.
In case of a minor sector draw in circle of the triangle formed by the two radii and the corresponding chord.
I think the inscribed circle of a minor sector is the one constructed in the attached figure, not the one as specified in the previous answer.