Question

If the points $a(4,3)$ and $b(x,5)$ are on a circle with center $O(2,3)$, then find the value of $x$ ?

Answer 1

Given, points are $A(4,3)$ and $B(x,5)$

Centre $O=(2,3)$

Radius$=$Distance between $A$ and $O=$Distance between $B$ and $O$

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

$\Rightarrow \sqrt{4+0^2}=\sqrt{x^2-4x+4+4}$

$\Rightarrow \sqrt{4}=\sqrt{x^2-4x+8}$

$\Rightarrow 4=x^2-4x+8$

$\Rightarrow x^2-4x+8-4=0$

$\Rightarrow x^2-4x+4=0$

$\Rightarrow (x-2{)}^2=0$

$\Rightarrow x=2$

Hence, the value of $x$ is $2$