intuitively, when you take B so far, the lines will have to less "steep" to be tangent to circle so the angle between them will also decrease.
so when you take B closer, [tex] m\angle GBD [/tex] increases
not sure if C lies on the line joining B and center, but if it does,
then again you can visualise that when the point is Far, the intersection points are more distant, reducing the angle
and when the point is very close to circle, the tangents $m\angle GCD$ will increase
and at extreme, when B is on the circle, it will become a straight line, and $\angle GCD$ wil become $180^{\circ}$
so it increases when you move closer. hence option 2
