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-​

Answer 1

Step-by-step explanation:

The tangents PQ and RS meet at X. The point lies on the circumference and we know that any diameter subtends a rt. angle at any pt. X on the circumference.

∴ tan θ=$\frac{PQ}{2r}$, tan(90°-θ)=$\frac{RS}{2r}$

∴ tan θ cot θ=$\frac{PQ.RS}{4r^2}$⇒$2r=\sqrt{PQ.RS}$

Hence, $d=2r=\sqrt{PQ.RS}$

Answer:

A) $\sqrt{PQ.RS}$