Am stuck on this question from first chapter of pure math by backhouse

[Kitimbo]

Find the circumcentre of the triangle with vertices (-3,0),(7,0),(9,-6).show that the point (1,2)lies on the circumcircle.
I could find the circumcentre,but how can I show that that point lies on the circumcircle.

 

[MarkFL]

Given that you have found the circumcenter is at:

\(\displaystyle (h,k)=(2,-5)\)

And the equation of the circumcircle is:

\(\displaystyle (x-2)^2+(y+5)^2=50\)

Then plug in the given point to see if an identity is obtained:

\(\displaystyle (1-2)^2+(2+5)^2=50\)