A circle C of radius 2 lies in the second quadrant and touches bo… | JEE Main 2025 Mathematics PYQ

MCQMediumJEE Main 2025 · 22 January, Shift 1Circle Equation & Properties

A circle C of radius $2$ lies in the second quadrant and touches both the coordinate axes. Let $r$ be the radius of a circle that has centre at the point $\left(2, 5\right)$ and intersects the circle C at exactly two points. If the set of all possible values of $r$ is the interval $\left(\alpha, \beta\right)$ , then $3\beta - 2\alpha$ is equal to:

A
$15$
B
$14$
C
$12$
D
$10$

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