From a point P outside a circle with centre at C, tangents PA and PB are drawn such that `1/(CA)^2+ 1/(PA)^2=1/16`, then the length of chord AB is

Options

A. 6
B. 8
C. 4
D. 12

Answer

B

Explanation

`tan theta = (r )/(PA)`
Given, `(1)/(r^(2)) +(1)/(PA^(2)) =(1)/(16)`

`rArr (cot^(2) theta+1)/((PA)^(2)) =(1)/(16)`
`rArr PA sin theta = 4 = x rArr 2x =8`.