Let `P Qa n dR S` be tangent at the extremities of the diameter `P R` of a circle of radius `rdot` If `P Sa n dR Q` intersect at a point `X` on the circumference of the circle, then prove that `2r=sqrt(P Q x R S)` .

Options

A. `sqrt(PQ.RS)`
B. `(PQ+RS)/(2)`
C. `(2PQ.RS)/(PQ+RS)`
D. `sqrt(PQ^(2)+RS^(2))/(2)`

Answer

A

Explanation

From figure, it is clear that `Delta PRQ and Delta RSP` and similar.

`therefore(PR)/(RS)=(PQ)/(RP)`
`rArrPR^(2)=PQ*RS`
`rArrPR=sqrt(PQ*RS)`
`rArr 2r=sqrt(PQ*RS)`