Let C₁ be the circle in the third quadrant of radius 3, that touc… | JEE Main 2025 Mathematics PYQ

MCQMediumJEE Main 2025 · 7 April, Shift 1Circle Equation & Properties

Let $C_1$ be the circle in the third quadrant of radius $3$ , that touches both coordinate axes. Let $C_2$ be the circle with center $(1, 3)$ that touches $C_1$ externally at the point $(\alpha, \beta)$ . If $(\beta - \alpha)^2 = \frac{m}{n}$ , and $\gcd(m, n) = 1$ , then $m + n$ is equal to:

A
$9$
B
$13$
C
$22$
D
$31$

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