Question: Tangents drawn from the point $P(1, 8)$ to the circle $x^2 + y^2 -6x -4y -11=0$ touch the circle at the points $A$ and $B$. What is the equation of the circumcircle of the triangle $PAB$?
I tried drawing a diagram, and found the length of the tangent. However, I lost as to where to proceed from there. Please help me!
Hint: The usual way to construct tangents to a circle around $C$ through a point $P$ is to draw a circle with diameter $CP$, and intersect that with the original circle. Any triangle made from three points on a circle has that circle as a circumcircle.