Circles – Assertion and Reason Questions

Q 1 :

Assertion (A): The tangents drawn at the end points of a diameter of a circle, are parallel.

Reason (R): Diameter of a circle is the longest chord.

Both, Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).
Both, Assertion (A) and Reason (R) are true but Reason (R) is not correct explanation for Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.

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(2)

Assertion: Two parallel tangents always lie at the end points of the diameter of the circle.

Reason: Diameter is the longest chord of a circle which passes through centre joining the two points on the circumference of a circle.

Both, Assertion (A) and Reason (R) are true but Reason (R) is not correct explanation for Assertion (A).

Q 2 :

Assertion (A): TA and TB are two tangents drawn from an external point T to a circle with centre ‘O’. If $∠ T B A = 75 °$ then $∠ A B O = 25 °$ .

Reason (R): The tangent drawn 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 the correct explanation of the Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.

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(4) Assertion (A) is false, but Reason (R) is true.

Q 3 :

Assertion (A): The tangents drawn at the end points of a diameter of a circle are parallel.

Reason (R): Diameter of a circle is the longest chord.

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.

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(2)

As PQ and AB are tangents and OD and OC are radius of the circle,

$O D ⟂ P Q a n d O C ⟂ A B$

⇒ ∠ODP = ∠OCA = 90°

∴ ∠ODP + ∠OCA = 180°

⇒ ∠ODP and ∠OCA are co-interior angles.

⇒ PQ and AB are parallel.

Assertion is true.

Also, diameter of a circle is the longest chord.

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

Q 4 :

Assertion (A): A tangent to a circle is perpendicular to the radius through the point of contact.

Reason (R): The lengths of tangents drawn from an external point to a circle are equal.

Both, Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).
Both, Assertion (A) and Reason (R) are true but Reason (R) is not correct explanation for Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.

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(2)

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

Q 5 :

Assertion (A): The angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segments joining the points of contact to the centre.

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

Both, Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).
Both, Assertion (A) and Reason (R) are true but Reason (R) is not correct explanation for Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.

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(1)

Let PA and PB be two tangents drawn from an external point P to the circle with centre O, as shown in Fig

$P A ⊥ O A and P B ⊥ O B$

$(T a n g e n t s a r e p e r p e n d i c u l a r t o t h e r a d i u s a t p o i n t o f c o n t a c t .)$

$I n q u a d r i l a t e r a l O A P B, w e h a v e :$

$∠ O A P + ∠ A P B + ∠ P B O + ∠ A O B = 360 °$

$\Rightarrow 90 ° + ∠ A P B + 90 ° + ∠ A O B = 360 °$

$\Rightarrow ∠ A P B + ∠ A O B = 180 °$

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

Topic Question Set

Q 1 :

Assertion (A): The tangents drawn at the end points of a diameter of a circle, are parallel.

Reason (R): Diameter of a circle is the longest chord.

Q 2 :

Assertion (A): TA and TB are two tangents drawn from an external point T to a circle with centre ‘O’. If $∠ T B A = 75 °$ then $∠ A B O = 25 °$ .

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

Q 3 :

Assertion (A): The tangents drawn at the end points of a diameter of a circle are parallel.

Reason (R): Diameter of a circle is the longest chord.

Q 4 :

Assertion (A): A tangent to a circle is perpendicular to the radius through the point of contact.

Reason (R): The lengths of tangents drawn from an external point to a circle are equal.

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