CAT 2018 Question Paper Shift 1 Solved Paper

It is given that radius of the circle =1cm
Chord AB subtends an angle of 60∘ on the centre of the given circle. R be the region bounded by the radii OA,OB and the arc AB.
Therefore, R=‌

60∘

360∘

× Area of the circle =‌

1

6

×π×(1)2=‌

π

6

sq. cmIt is given that OC=OD and area of triangle OCD is half that of R. Let OC=OD=x.
Area of triangle COD=‌

1

2

×OC×OD×sin‌60°
‌

π

6×2

=‌

1

2

×x×x×‌

√3

2

⇒x2=‌

π

3√3

⇒x=(‌

π

3√3

)‌

1

2

cm