Two equal chords AB and AC of the circle `x^2 +y^2-6x -8y-24 = 0` are drawn from the point `A(sqrt33 +3,0)`. Another chord PQ is drawn intersecting AB and AC at points R and S, respectively given that `AR=SC=7` and RB = AS = 3 . The value of `PR/QS` is

Options

A. 1
B. 1.5
C. 2
D. None of these

Answer

A

Explanation

Point `A(sqrt(33)+3,0)` lies on the given circle,
`x^(2)+y^(2)-6x-8y -24 =0`.
PQ and AB intersect inside the circle.
Let `PR = a, RS = b, QS =c`
Since `PR xx RQ = AR xx RB`
`rArr a(b+c) = 3xx 7`
Also, `QS xx SP = 3 xx7`
`rArr c (a+b) =3xx 7`
`rArr a =c`
`:. PR//QS =1`