The diagram shows three points A, B and C on a circle, centre O and radius 10 cm. The line AD is a tangent to the circle. Given that angle AOB = 60°, find, to one decimal place, (a) the length of the arc ACB, (b) the area of the segment ACB. Given also that the length of AD equals the length of the arc ACB, find (c) the area of the shaded region ACBD, (d) the length of BD.​