Circumcentre of the triangle formed by the points (2, 3), (0, 1), (4, 1) is

Let A (2, 3), B(0, 1), C (4, 1)

Slope of AB $=\frac{1-3}{0-2}=1$

$\begin{array}{l}SlopeofBC=\frac{1-1}{4-0}=0\\ SlopeofAC=\frac{1-3}{4-2}=-1\\ SlopeofAB\times SlopeofAC=-1\\ \angle A={90}^0\Rightarrow {\Delta }^{le}isRightangle\\ \therefore Circumcentre=Midpo\mathrm{int}\overline{BC}\\ \Rightarrow \left(\frac{0+4}{2},\frac{1+1}{2}\right)\\ =\left(2,1\right)\end{array}$