A circular ring of radius 3cm hangs horizontally form a point 4cm vertically above the centre by 4 strings attached at equal intervals to its circumference. If the angle between two consecutive strings be `theta` , then `costheta` is equal to `4/5` (b) `4/(25)` (d) `(16)/(25)` (d) none of these

Options

A. `(4)/(5)`
B. `(4)/(25)`
C. `(16)/(25)`
D. none of these.

Answer

C

Explanation

`OP=4`
`OA=OB=OC=OD=3`
`AP=BP=CP=DP=sqrt(3^(2)+4^(2))=5`
ABCD is a square of side length `(6)/sqrt(2)=3sqrt(2)`.

`sin((theta)/(2))=((1)/(2)BC)/(BP)=((3)/sqrt(2))/(5)=(3)/(5sqrt(2))`
`therefore cos theta=1-2sin^(2)((theta)/(2))=(16)/(25))`