Assertion (A) & Reason (B) MCQ

MCQ 11 Mark

Assertion $(A) :$ In the given figure, $a$ quad. $ABCD$ is drawn to circumscribe a given circle as shown.

Reason $(R) :$ In two concentric circles, the chord of the larger circle, which to uches the smaller circle, is bisected at 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.
✓
Assertion $(A)$ is false and Reason $(R)$is true.

Answer

Correct option: D.

Assertion $(A)$ is false and Reason $(R)$is true.

The Assertion $(A)$ is false since sum of the opposite sides of a quadrilateral circumscribing a circle are equal, and not the adjacent sides.
The chord of the larger circle is the tangent to the smaller circle.
We know that the perpendicular drawn from the centre to the chord
So, the Reason $(R)$ is true.
But is not the correct explanation for the Assertion $(A)$.

View full question & answer→

MCQ 21 Mark

Assertion $(A)$ : If two tangent are drawn to a circle from an external point then they subtend equal angles at the centre.
Reason $(R)$ : 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)
$\angle\text{B}=\angle\text{C}=90^\circ$
$\Rightarrow\triangle\text{OBA}\cong\triangle\text{OCA}$ ....(RHS congruence criterion)
So, $\angle\text{OBA}=\angle\text{COA}$ ....(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 $(A)$.

View full question & answer→

MCQ 31 Mark

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

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

Solution:

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

View full question & answer→

Maths Assertion (A) & Reason (B) MCQ

Test yourself on this topic