Question

Assertion (A)
At point P of a circle with centre O and radius 12 cm, a tangent PQ of length 16 cm is drawn. Then, OQ = 20 cm.

Reason (R)
The tangent at any point of a circle is perpendicular to the radius through the point of contact.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R)is true.

Answer 1

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

$$\begin{gathered} \mathrm{In}∆OPQ,\angle OPQ={90}^0. \\ \therefore O{Q}^2=O{P}^2+P{Q}^2 \\ \Rightarrow OQ=\sqrt{O{P}^2+P{Q}^2} \\ =\sqrt{{12}^2+{16}^2} \\ =\sqrt{144+256} \\ =\sqrt{400} \\ =20\mathrm{cm} \end{gathered}$$