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

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.\

Professor PC Thomas Classes · Answer

(c): Clearly, reason $(\mathrm{R})$ is false as centre of a circle is the mid-point of diameter of the circle.\ Now, as $A(4,3)$ and $B(x, 5)$ lie on a circle, so distance between $O$ and $A=$ distance between $O$ and $B$.\[0pt] [ ∵ Radii of a circle]\ $\Rightarrow \sqrt{(4-2)^{2}+(3-3)^{2}}=\sqrt{(x-2)^{2}+(5-3)^{2}}$\ Squaring both sides, we get $(2)^{2}=(x-2)^{2}+(2)^{2}$\ $\Rightarrow \quad(x-2)^{2}=0 \Rightarrow x=2$\ $\therefore \quad$ Assertion (A) is true.\