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Circle question

2025 · 7 Apr · Shift 1 · Q27
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  5. /2025 · 7 Apr · Shift 1 · Q27

Circle question

2025 · 7 Apr · Shift 1 · Q27

JEE MainMathematicsCircleMCQ+4 / −1
Let C1C_1C1​ be the circle in the third quadrant of radius 3 , that touches both coordinate axes. Let C2C_2C2​ be the circle with centre (1,3)(1,3)(1,3) that touches C1\mathrm{C}_1C1​ externally at the point (α,β)(\alpha, \beta)(α,β). If (β−α)2=mn(\beta-\alpha)^2=\frac{m}{n}(β−α)2=nm​, gcd⁡(m,n)=1\operatorname{gcd}(m, n)=1gcd(m,n)=1, then m+nm+nm+n is equal to
  1. A
    22
  2. B
    13
  3. C
    9
  4. D
    31
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