MCQ
Each question consists of two statements, namely, Assertion $(A)$ and Reason $(R)$. for selecting the correct answer, use the following code:
Assertion $(A)$
Reason $(R)$
 
At a point $P$ of a circle with centre $O$ and radius $12cm$, a tangent $PQ$ of length $16\ cm$ is drawn. Then, the point of contact. $OQ = 20\ cm.$
The tangent at any point of a circle is perpendicular to the radius through the point of contact.
  • 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

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

We know that the tangent is perpendicular to the radius of a circle.
In $\triangle\text{OPQ},$
By Pythagoras theorem,
$OQ^2= QP^2 + OP^2$
$\Rightarrow OP^2 = 16^2 + 12^2$
$\Rightarrow OP^2 = 256 + 144$
$\Rightarrow OP^2 = 400$
$\Rightarrow OP = 20\ cm$
So, the Assertion $(A)$ is true.
The Reason $(R)$ is true and is the correct explanation for the Assertion $(A).$
 

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