The main question is as follows :
Find the point $P$, such that $P$ is the centre of a circle circumscribing the triangle whose angular points are $(1,1), (2,3), (-2,2)$.
My method :
I am completely new to Coordinate geometry of higher level. I understood what the question asks, it asks me to find the circumcenter of the triangle, but all the formulae given to me are very confusing. I'm having trouble proceeding further. Please help me.
The general equation of a cirlce with the center $x_0,y_0$ and radius $R$ is:
$$(x-x_0)^2+(y-y_0)^2=R^2$$
You know three points which lie on the circle. Thus, you can create a system of three equations to find the three unknowns $x_0,y_0,R$:
$$ \begin{cases} (1-x_0)^2+(1-y_0)^2=R^2 \\ (2-x_0)^2+(3-y_0)^2=R^2 \\ (-2-x_0)^2+(2-y_0)^2=R^2 \end{cases}$$