**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

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):** Centre of a circle is the mid-point of each chord of the circle.

Accepted Answer

Step 1: $OA = \sqrt{(4-2)^2 + (3-3)^2} = 2$. For $B$ on circle: $OB = 2 \Rightarrow (x-2)^2 + 4 = 4 \Rightarrow x = 2$. A is true. R is false — centre is the mid-point of a diameter, not every chord.

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Solution