find the circumcentre the triangle formed by A(1,2) B(-2,2)

,C(1,5),

Given points are,
A(1,2) B(-2,2) ,C(1,5)
To find out the circumcenter we have to solve any two bisector equations and find out the intersection points.

So, mid point of AB = ((1-2) / 2 , (2 + 2) / 2) = (-0.5,2)

Slope of AB = ((-3/2) / 0) = Not defined
Slope of the bisector is the negative reciprocal of the given slope.
So, the slope of the perpendicular bisector =0
Equation of AB is
y=2………………(1)
Similarly, for AC
Mid point of AC = (1,3.5)

Slope of AC =0
Slope of the bisector is the negative reciprocal of the given slope.
So, the slope of the perpendicular bisector = -3/0
Equation of AC is

x=1………………(2)
By solving equation (1) and (2),
x = 1
Substitute the value of x in to (1)
y = 2
So the circumcenter is (1, 2)