A sector `O A B O` of central angle `theta` is constructed in a circle with centre `O` and of radius `6.` The radius of the circle that is circumscribed about the triangle `O A B ,` is `6costheta/2` (b) `6sectheta/2` `3sectheta/2` (d) `3(costheta/2+2)`

Options

A. `6 cos.(theta)/(2)`
B. `6 sec.(theta)/(2)`
C. `3 sec.(theta)/(2)`
D. `3 (cos.(theta)/(2) + 2)`

Answer

C

Explanation

Let the required radius be R
`:. R = (abc)/(4Delta), Delta = (1)/(2) .6.6. sin theta = 18 sin theta`

and `a = b = 6`
Now, `sin.(theta)/(2) = (c)/(12)`
`rArr c = 12 sin.(theta)/(2)`
`:. R = (36.12 sin (theta//2))/(4.18. sin theta) = 3 sec.(theta)/(2)`