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

Question:

If the points A(4, 3) and B(x, 5) lie on the circle with centre O(2, 3), find the value of x.

Solution:

The given points $A(4,3)$ and $B(x, 5)$ lie on the circle with centre $O(2,3)$.

Then, $O A=O B$

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

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

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

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

$\Rightarrow x-2=0$

$\Rightarrow x=2$

Hence, the value of $x=2$.