Let S be a circle with centre O and radius 2. A and B be two points on the circle. A O B=x , tangents at A and B intersect at D and O A and B D intersect at C . Then which of the following must be correct?

Step-by-step solution

r=2 aligned & A D=r x 2 =B D & Area ( O B C)= 1 2 r^2 x and Area ( O A B)= 1 2 r^2 x & _ x 0 Area ( O B C) Area ( O A B) =1 & Area ( A D B)= 1 2 A D B D ( -x)= 1 2 r^2 ^2 x 2 x & _ x 0 Area ( A B D) ( Area ( O A B))^3 = _ x 0 1 2 r^2 ^2 x 2 x ( 1 2 r^2 x )^3 & = _ x 0 4 r^2 ^2 x 2 r^6 ^2 x = _ x 0 4 ^2 x 2 16 4 ^2 x 2 ^4 x 2 = 1 16 aligned