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Let P Q and R S be tangent at the extre...

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)` .

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`(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)`
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