Mathematics - Circle Question with Solution | TestHub

Equation of the line passing through the points $(2,3)$ and $(4,5)$ is $$y-3=\left(\frac{5-3}{4-2}\right)x-2\Rightarrow x-y+1=0$$ Equation of the perpendicular line passing through the midpoint $(3,4)$ is $x+y-7=0$ Lines (1) and (2) intersect at the center of the circle. So, the center of the circle is $(3,4)$ Therefore, the radius is $$\begin{array}{rl}& \sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ & =\sqrt{(2-3{)}^2+(3-4{)}^2}=\sqrt{2}\text{ units. }\end{array}$$