<s>[INST] What is the equation of the circle I've been experiencing a difficulties in answering this. I hope someone will help me in solving this
Find the equation of the circle through the points $(2,8),(7,3)$ and $(-2,0)$.
 [/INST] 
The question can be restated as

Given triangle $ABC$ with coordinates of vertices $A=(-2,0)$,
$B=(7,3)$, $C=(2,8)$, find the equation of its circumscribed circle.

First, find the squares of the side lengths of $\triangle ABC$:
\begin{align}
a^2&=50
,\quad
b^2= 80
,\quad
c^2=90
\tag{1}\label{1}
.
\end{align}
Second, the coordinates of the circumcenter
is known to be found as
\begin{align}
O&=
\frac{a^2(b^2+c^2-a^2)\cdot A+b^2(a^2+c^2-b^2)\cdot B+c^2(b^2+a^2-c^2)\cdot C}
{a^2(b^2+c^2-a^2)+b^2(a^2+c^2-b^2)+c^2(b^2+a^2-c^2)}
\\
&=\tfrac1{12}\cdot(5\,A+4\,B+3\,C)
=\tfrac1{12}\cdot(5\,(-2,0)+4\,(7,3)+3\,(2,8))
=(2,3)
\tag{2}\label{2}
.
\end{align}
Third, find the radius:
\begin{align}
R&=|O-A|=|O-B|=|O-C|=5
\tag{3}\label{3}
.
\end{align}
Hence, the equation of the circle is
\begin{align}
(x-2)^2+(y-3)^2&=25
\tag{4}\label{4}
.
\end{align}
</s>