In the circle above, if OA and BC are parallel, and radius OA of the

Given
(i) OA=OB=OC=OD=radius of circle=3 unit (It is infered that OBC is an isosceles triangle)
(ii)OA||BC
(iii) \(\angle{OCD}\)=60 degree
To find: Length of Minor arc AD ? (Minor arc=Arc AXD in figure) (Our aim is to determine \(\angle{AOD}\))
Refer to the enclosed figure, we have \(\angle{OBC}=30\) (As per given data(i))
We have \(\angle{AOB}=\angle{OBC}=30\) (As per given data (ii)) (OA||BC; so alternate angles are equal)
Also we have \(\angle{BOD}=180=\angle{AOB}+\angle{AOD}\) (supplementary angles; angles on a straight line(here diameter))
So, \(\angle{AOD}=180-30=150\)

Now, Arc AXD=\(2πr*\frac{150}{360}\)=\(2π*3*\frac{5}{12}\)=\(\frac{5}{2}\pi\)

Ans. (C)