Equation of circumcircle From a point $(a,b)$ two tangents $\overset{\leftrightarrow}{PQ}$ and $\overset{\leftrightarrow}{PR}$ are drawn to a circle 
$x^2 + y^2 - a^2=0$
Find the equation of the circumcircle of $\triangle PQR$.
My attempt:
The circumcircle and the given circle have a common chord $\overline{QR}$.
Apart from this I could not convert this into useful information.

$$x^2+y^2-a^2=0\ \ \ \ (0)$$
Using  The equation of a pair of tangents to a circle from a point.
tangents-to-a-circle-from-a-point,
the equation of the pair of tangents, $$(a^2+b^2-a^2)(x^2+y^2-a^2)=(ax+by-a^2)^2\ \ \ \ (1)$$ 
Now the equation of any conic passing through the intersection of $(0),(1)$ 
will be $$(a^2+b^2-a^2)(x^2+y^2-a^2)-(ax+by-a^2)^2+K(x^2+y^2-a^2)=0\ \ \ \  (2)$$  where $K$ is an arbitrary constant.
Now $(2)$ has to pass through $(a,b)$ 
