Question:
If the points A(4, 3) and B(x, 5) lie on a circle with centre O(2, 3), find the value of x.
Solution:
Given, the points A(4, 3) and B(x, 5) lie on a circle with centre O(2, 3).
Then OA = OB
Also (OA)2 = (OB)2
$\Rightarrow(4-2)^{2}+(3-3)^{2}=(x-2)^{2}+(5-3)^{2}$
$\Rightarrow(2)^{2}+(0)^{2}=(x-2)^{2}+(2)^{2}$
$\Rightarrow 4=(x-2)^{2}+4$
$\Rightarrow(x-2)^{2}=0$
$\Rightarrow x-2=0$
$\Rightarrow x=2$
Therefore, x = 2.