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.

HINT:
The equation of tangent at $P(a\cos2t,a\sin2t)$ is $$x\cos2t+y\sin2t=a$$
Now if this passes through $(a,b),$
$$a\cos2t+b\sin2t=a\iff2b\sin t\cos t=a(2\sin^2t)\implies$$
either $\sin t=0\implies P_1(a,0)$
or $\tan t=\dfrac ba\implies P_2\left(a\cdot\dfrac{a^2-b^2}{a^2+b^2},\dfrac{2a^2b}{a^2+b^2}\right)$
We already have $$Q(a,b)$$
Now use this
