Two circles of radii 3.5 and 4.2 cm with centres O1 and O2 intersect at points A and B as shown. The distance between the two centres is 6 cm. Calculate: (a) The size of angle AO1B. (b) The size of angle AO2B. (c) The area of quadrilateral O1AO2B. (d) The shaded area.

Step 1: Identify the given information from the problem.
Radius of circle with centre $O_1$ is $r_1 = O_1A = O_1B = 3.5$ cm.
Radius of circle with centre $O_2$ is $r_2 = O_2A = O_2B = 4.2$ cm.
Distance between centres $O_1O_2 = 6$ cm.
Points A and B are the intersection points of the two circles.

a) The size of $\angle AO_1B$ (to the nearest degree)
Consider the triangle $\triangle AO_1O_2$. The sides are $O_1A = 3.5$ cm, $O_