jee-main 2023 Q64

jee-main · India · session1_31jan_shift1 Circles Area and Geometric Measurement Involving Circles

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 $C_1$ in $T$. 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) $22 + \sqrt{2}$
(2) $41 + \sqrt{2}$
(3) $3 + 2\sqrt{2}$
(4) $21 + \sqrt{2}$

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 $C_1$ in $T$. 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) $22 + \sqrt{2}$\\
(2) $41 + \sqrt{2}$\\
(3) $3 + 2\sqrt{2}$\\
(4) $21 + \sqrt{2}$

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