The combined equation of the pair of tangents from an external point (x1,y1) to circle S=0 is $T^2$ = SS1. Here S is the circle equation with (x,y), T is the tangent equation at (x1,y1) with (x,y), and S1 is the value at (x1,y1). The angle between the tangents is 2tan^(-1)$\frac{r}{L}$ where L=sqrt(S1) is the tangent length and r is the radius.