JEE Math Practice Question

Let a circle $$C_{1}$$ be obtained on rolling the circle $$x^{2}+y^{2}-4 x-6 y+11=0$$ upwards 4 units on the tangent $$\mathrm{T}$$ to it at the point $$(3,2)$$. Let $$C_{2}$$ be the image of $$C_{1}$$ in $$\mathrm{T}$$. Let $$A$$ and $$B$$ be the centers of circles $$C_{1}$$ and $$C_{2}$$ respectively, and $$M$$ and $$N$$ be respectively the feet of perpendiculars drawn from $$A$$ and $$B$$ on the $$x$$-axis. Then the area of the trapezium AMNB is :

1. A.$$2\left( {2 + \sqrt 2 } \right)$$
2. B.$$4\left( {1 + \sqrt 2 } \right)$$
3. C.$$3 + 2\sqrt 2 $$
4. D.$$2\left( {1 + \sqrt 2 } \right)$$