Let PQ and RS be tangents at the extremities of the diameter PR of a circle of radius r. If PS and RQ intersect at a point X on the circumference of the circle, then 2r equals

Options

A. `sqrt(PQ xx RS)`
B. `sqrt(PQxxRS)/(2)`
C. `(2PQxxRS)/(2)`
D. `(sqrt(PQ^(2)xxRS^(2)))/(2)`

Answer

A

Explanation

In fig. , we have
`tan theta = (RS)/(PR) and tan ((pi)/(2)-0)=(PQ)/(PR)`
`rArr 1= (RS)/(PR)xx(PQ)/(PR)rArrPR=sqrt(PQ xx RS)`