Mathematics

Problem

Let a circle

C_1

be obtained on rolling the circle

x^2 + y^2 - 4x - 6y + 11 = 0

upwards 4 units on the tangent

T

to it at the point

(3, 2)

. Let

C_2

be the image of

C_1

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: [Main Jan. 31, 2023 (I)] (a)

2(2 + \sqrt{2})

(b)

4(1 + \sqrt{2})

(c)

3 + 2\sqrt{2}

(d)

2(1 + \sqrt{2})