Question

$A(4,3)$ & $B(x,5)$ on the circle with center $O(2,3)$ . Find $x$

Answer 1

Given:$A$ and $B$ lie on the circle and $O$ is the center of the circle.

$\therefore OA$ and $OB$ are radii of the circle.

$\therefore OA=OB$

$\Rightarrow \sqrt{{(2-4)}^2+{(3-3)}^2}=\sqrt{{(2-x)}^2+{(3-5)}^2}$

$\Rightarrow \sqrt{{\left(2\right)}^2+0}=\sqrt{{(2-x)}^2+{(-2)}^2}$

$\Rightarrow 4={(2-x)}^2+4$

$\Rightarrow 2-x=0$

$\therefore x=2$