QJEEAdv23Ma963e: JEE Advanced 2023 Mathematics - Class 11 JEEAdv23Ma963e Solution: Let be the circle of radius 1 with center at the origin. Let be …

Let $C_1$ be the circle of radius 1 with center at the origin. Let $C_2$ be the circle of radius $r$ with center at the point $A=(4,1)$ , where 1 < r < 3 . Two distinct common tangents $P Q$ and $S T$ of $C_1$ and $C_2$ are drawn. The tangent $P Q$ touches $C_1$ at $P$ and $C_2$ at $Q$ . The tangent $S T$ touches $C_1$ at $S$ and $C_2$ at $T$ . Mid points of the line segments $P Q$ and $S T$ are joined to form a line which meets the $x$ -axis at a point $B$ . If $A B=\sqrt{5}$ , then the value of $r^2$ is :