Answer:
Circumcenter is
.
Step-by-step explanation:
Given:
The three vertices of triangle OVW are
.
Circumcenter is a point inside the triangle which is equidistant from each of the vertices of the triangle.
Let
be the circumcenter.
Distance between two points
and
is given as:
![D=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}](https://tex.z-dn.net/?f=D%3D%5Csqrt%7B%28x_%7B2%7D-x_%7B1%7D%29%5E%7B2%7D%2B%28y_%7B2%7D-y_%7B1%7D%29%5E%7B2%7D%7D)
So, as per the definition of circumcenter, distance of point
from point
is equal to distance of point
from point
.
So, OC = VC
or ![(OC)^{2}=(VC)^{2}](https://tex.z-dn.net/?f=%28OC%29%5E%7B2%7D%3D%28VC%29%5E%7B2%7D)
.
Similarly, distance of point
from point
is equal to distance of point
from point
.
or
![(OC)^{2}=(WC)^{2}](https://tex.z-dn.net/?f=%28OC%29%5E%7B2%7D%3D%28WC%29%5E%7B2%7D)
.
Therefore, the circumcenter of the triangle with the given vertices is
.