Circle Tangency Point (Jee Mains)

Equation & Position in Circle

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Circle Tangency Point

Let C₁ be the circle in the third quadrant of radius 3, that touches both coordinate axes. Let C₂ be the circle with centre (1, 3) that touches C₁externally at the point (α, β). If (β - α)² = $\frac{m}{n}$ , gcd(m, n) = 1, then m + n is equal to :

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