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JEE Main202522 Jan 2025Morning ShiftMathematicsCircleActual

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 ( , ) , then 3 -2 is equal to :

Options

  1. A10
  2. B15
  3. C12
  4. D14

Correct answer

B. 15

Step-by-step solution

aligned & C₁ C₂= (2+2)^2+(5-2)^2 & = 16+9 & =5 & r+2>5 & r>3 & r < 5+2 & r < 7 & =3, =7 & 3 -2 =3(7)-2(3)=21-6=15 aligned

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