Answer: \((x-2)^2+(y+1)^2=74\).

Use the circle or sector formulae in radians. Where a tangent is involved, remember that the radius to the point of contact is perpendicular to the tangent.

The centre of the circle is the midpoint of \(AB\):

\(\left(\frac{-3+7}{2},\frac{6+(-8)}{2}\right)=(2,-1).\)

The radius is the distance from the centre to either endpoint, for example to \(A\):

\(r^2=(-3-2)^2+(6-(-1))^2=(-5)^2+7^2=74.\)

Therefore the equation of the circle is

\((x-2)^2+(y+1)^2=74.\)

This gives the required answer: \((x-2)^2+(y+1)^2=74\).