jee-main 2022 Q65

jee-main · India · session1_29jun_shift1 Circles Area and Geometric Measurement Involving Circles
Let the tangent to the circle $C _ { 1 } : x ^ { 2 } + y ^ { 2 } = 2$ at the point $M ( - 1,1 )$ intersect the circle $C _ { 2 }$ : $( x - 3 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 5$, at two distinct points $A$ and $B$. If the tangents to $C _ { 2 }$ at the points $A$ and $B$ intersect at $N$, then the area of the triangle $A N B$ is equal to
(1) $\frac { 1 } { 2 }$
(2) $\frac { 2 } { 3 }$
(3) $\frac { 1 } { 6 }$
(4) $\frac { 5 } { 3 }$
Let the tangent to the circle $C _ { 1 } : x ^ { 2 } + y ^ { 2 } = 2$ at the point $M ( - 1,1 )$ intersect the circle $C _ { 2 }$ : $( x - 3 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 5$, at two distinct points $A$ and $B$. If the tangents to $C _ { 2 }$ at the points $A$ and $B$ intersect at $N$, then the area of the triangle $A N B$ is equal to\\
(1) $\frac { 1 } { 2 }$\\
(2) $\frac { 2 } { 3 }$\\
(3) $\frac { 1 } { 6 }$\\
(4) $\frac { 5 } { 3 }$