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.

Answer 1

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
$$\begin{gathered} \Rightarrow {\left(4-2\right)}^2+{\left(3-3\right)}^2={\left(x-2\right)}^2+{\left(5-3\right)}^2 \\ \Rightarrow {\left(2\right)}^2+{\left(0\right)}^2={\left(x-2\right)}^2+{\left(2\right)}^2 \\ \Rightarrow 4={\left(x-2\right)}^2+4 \\ \Rightarrow {\left(x-2\right)}^2=0 \\ \Rightarrow x-2=0 \\ \Rightarrow x=2 \end{gathered}$$
Therefore, x = 2.