Question

Assertion (A): In the given figure, PQ is a tangent to a circle centred at O. If the radius of the circle is 5 cm then the length of the tangent PQ is \[\dfrac{5}{\sqrt{3}}\ \text{cm.}\]

Reason (R): If two tangents are drawn to a circle from an external point then they subtend equal angles at the centre.

विकल्प

• 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).

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

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

Answer 1

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

Explanation:

Step 1 – Assertion: A is false. The radius to the point of contact is perpendicular to the tangent. In the right triangle shown, `tan 30^circ = 5/(PQ)`, giving `PQ = 5sqrt(3)` cm, not `5/sqrt(3)` cm.

Step 2 – Reason: R is true. Tangents drawn from an external point are equal, so the corresponding right triangles formed with the radii are congruent; consequently, the tangents subtend equal angles at the centre.