If AD=18, then AC=9 and CD=9.
(i) Length of the minor arc BD is greater than 10.
$$Length\ of\ arc\ BD=2\pi r\ \frac{C}{360^0}$$
Where C = central angle and radius r = radius.
BC=CD= radius of the circle
Radius = 9 and angle c = 60 degrees.
$$Length\ of\ arc\ BD=2\pi\cdot9\cdot\ \frac{60}{360^0}=\ 3\pi\ =\ 9.42$$
(ii) In triangle ABD, angle B =90 degrees because triangle ABD is inside semicircle with one side AD as the diameter.
(iii) Triangle BCD is equilateral from the diagram shown in question. Angle A=30 degrees from (ii) above and Angle b=90 degrees. Hence, triangle ABD is in 30, 90 and 60 degrees respectively.
So, angle D=60 degrees; this thus make angle C = 60 degrees.
$$Therefore,\ \triangle BCD=equilateral\ triangle\ -\ 60^0,60^0,60^0$$
Thus, (i) is false. Only (ii) and (iii) are true. So, the correct answer is option D
Hope this helps?
