Question

If the points $A(4,3)$ and $B(x,5)$ are on the circle with center $O(2,3),$ find the vale of $x$.

Answer 1

Since $A$ and $B$ lie on the circle having centre $O$.

$\therefore AO=OB$ [radius of circle is same every where]

$\Rightarrow \sqrt{{(4-2)}^2+{(3-3)}^2}=\sqrt{{(x-2)}^2+{(5-3)}^2}$
$\Rightarrow \sqrt{2^2}=\sqrt{{(x-2)}^2+4}$
Squaring on both sides, we get
$\Rightarrow 4={(x-2)}^2+4$
$\Rightarrow {(x-2)}^2=0$
$\Rightarrow x-2=0$
$\therefore x=2$