Q1. [1]
Questions number 19 and 20 are Assertion and Reason based questions carrying 1 mark each. Select the correct answer from codes (a)–(d).
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) : Centre of a circle is the mid-point of each chord of the circle.
- (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
- (b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
- (c) Assertion (A) is true, but Reason (R) is false.
- (d) Assertion (A) is false, but Reason (R) is true.
Previously asked in CBSE board exam
2023 30/5/1 Q19
Generated by claude-sonnet-4-6 · 2026-06-15 10:24 · grounding rag
Model Answer
(c) Assertion (A) is true, but Reason (R) is false.
Since OA = OB (radii), $\sqrt{(4-2)^2+(3-3)^2} = \sqrt{(x-2)^2+(5-3)^2}$ gives $2 = \sqrt{(x-2)^2+4}$, so $x = 2$. ✓
The centre is NOT the mid-point of every chord; it bisects a chord only when the line from centre is perpendicular to it.
Explanation
- Assertion check: OA = $\sqrt{4+0}$ = 2; OB = $\sqrt{(x-2)^2+4}$ = 2 ⟹ $(x-2)^2$ = 0 ⟹ $x = 2$. True.
- Reason check: The centre is the mid-point of a chord only if it is the perpendicular bisector of that chord — it is not the mid-point of every chord. The statement as given is false.
- So the answer is (c): A is true, R is false.
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