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Jee Main 2025 — Medium JEE math MCQ

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 \((2, 5)\) and intersects the circle \(C\) at exactly two points. If the set of all possible values of \(r\) is the interval \((\alpha, \beta)\), then \(3\beta - 2\alpha\) is equal to
  1. A. \(10\)
  2. B. \(15\)
  3. C. \(12\)
  4. D. \(14\)

Solution

The correct option is **B**. (B. \(15\))

MATH

medium • PYQ Reworded
Question
Read carefully, then pick the best option.
A circle CC of radius 2 lies in the second quadrant and touches both the coordinate axes. Let rr be the radius of a circle that has centre at the point (2,5)(2, 5) and intersects the circle CC at exactly two points. If the set of all possible values of rr is the interval (α,β)(\alpha, \beta), then 3β−2α3\beta - 2\alpha is equal to
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Jee Main 2025 — Medium JEE Mathematics MCQ | MyGoalPrep