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

Explanation

`(PQ)/(PR)=tan(90-theta)=cottheta-(1)`

`(RS)/(PR)=tantheta-(2)`

Multiplying equation 1 and 2

`(PQ)/(PR)*(RS)/(PR)=cottheta*tantheta=1`

`PQ*RS=PR^2`

`PQ*RS=(2r)^2`

`2r=sqrt(PQ*RS)`