Question

Assertion (A): If the points $$A(4,3)$$ and $$B(x, 5)$$ lie on a circle with centre $$O(2, 3)$$ then the value of $$x$$ is 2.

Reason (R): The centre of a circle is the midpoint of each chord of the circle.

Options

• 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 true and Reason (R) is false.

Explanation:

Step 1 – Assertion: A is true. Since $$A(4, 3)$$ is on the circle with centre $$O(2, 3)$$, the radius is 2. For $$B(x, 5)$$ to be on the same circle, its distance from the centre must also be 2: $$(x - 2)^2 + (5 - 3)^2 = 2^2$$ $$(x - 2)^2 = 0 \Rightarrow x = 2$$

Step 2 – Reason: R is false. The centre does not bisect every chord; it bisects a chord only when the perpendicular from the centre meets that chord.