SATHEE: Circle 3 Question 9

Circle 3 Question 9

9. Let $P Q$ and $R S$ be tangents 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 $2 r$ equals

(2001, 1M)

(a) $\sqrt{P Q \cdot R S}$

(b) $\frac{P Q + R S}{2}$

(d) $\sqrt{\frac{P Q^{2} + R S^{2}}{2}}$

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Answer:

Correct Answer: 9. (a)

Solution:

From figure, it is clear that $△ P R Q$ and $△ R S P$ are similar.

$\begin{aligned} ∴ \frac{P R}{R S} = \frac{P Q}{R P} \\ \Rightarrow P R^{2} = P Q \cdot R S \\ \Rightarrow P R = \sqrt{P Q \cdot R S} \\ \Rightarrow 2 r = \sqrt{P Q \cdot R S} \end{aligned}$

Circle 3 Question 9

9. Let $P Q$ and $R S$ be tangents 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 $2 r$ equals

Answer:

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Circle 3 Question 9

9. 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:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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9. Let $P Q$ and $R S$ be tangents 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 $2 r$ equals