Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$\alpha +\beta =\frac{\pi }{2}$
$tan\alpha tan\beta =1$
$\frac{RS}{PR}\times \frac{PQ}{PR}=1$
$(PR{)}^2=RS.PQ$
$PR=\sqrt{RS.PQ}$
$2r=\sqrt{RS.PQ}$