Consider a circle of radius R. What is the lengths of a chord which subtends an angle `theta` at the centre ?

Options

A. `2R sin(theta/2)`
B. `2R sin theta`
C. `2R tan (theta/2)`
D. `2R tan theta`

Answer

A

Explanation

Let three be a circleof radius R and chord AB.
`OD_|_AB` and `AD = DB`.
and `AD = 2AD`.
`angle(AOB) = theta`
`rArr angle(AOD) = theta/2`
In `DeltaAOD`,
`sin'(theta)/(2) = (AD)/(OA)`
`sin'(theta)/(2) = (AD)/(R )`
`AD = Rsin '(theta)/(2)`
`:.` Length of chord `AB = 2 AD = 2 R sin '(theta)/(2)`.