Each question consists of two statements, namely, Assertion (A) a… - Vidyadip

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 $(R)$
If two tangent are drawn to a circle from an external point then they subtend equal angles at the centre.	A parallelogram circumscribing a circle is a rhombus.

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

Both Assertion $(A)$ and Reason $(R)$ are true but Reason $(R)$ is not a correct explanation of Assertion $(A).$

Consider tangent $AB$ and $AC$ drawn to the circle with centre $O$.
In $\triangle\text{OBA}$ and $\triangle\text{OCA},$
$\text{AO}=\text{AO} ....($common side$)$
$\text{OB}=\text{OC} .....($radii of the same circle$)$
$\angle\text{B}=\angle\text{C}=90^\circ$
$\Rightarrow\triangle\text{OBA}\cong\triangle\text{OCA} ....(\text{RHS}$ congruence criterion$)$
So, $\angle\text{OBA}=\angle\text{COA} ....(\text{cpct})$
Thus, the $(R)$ is also true and can be proved using the property, 'tangent from an external point to a circle are equal'
But, the Reason $(R)$ is not the correct explanation for the Assertion $(A).$

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