AB is a diameter of the circle. C lies on AB and AC = 4 cm. Use a straight edge and compasses only.

(a(i)) Construct the locus of points equidistant from A and B. [2]

(a(ii)) Construct the locus of points 4 cm from C. [1]

(b) Shade the region inside the original circle that is nearer to B than to A and less than 4 cm from C. [1]