If \( \theta \) is the angle between the pair of tangents drawn from the point \((0,\frac{7}{2})\) to the circle \(x^2 + y^2 - 14x + 16y + 88 = 0\), then \(\tan \theta\) equals

Circle centre (7,-8), r^2=49+64-88=25, r=5. Distance^2 from (0,7/2) = 49+132.25=181.25, tangent length = sqrt(156.25)=12.5. tan(theta/2)=5/12.5=2/5, tan(theta)=(4/5)/(1-4/25)=20/21.