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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 centre (1, 3) that touches C 1 externally at the point ( α , β ). If ( β−α ) 2 = n m , gcd(m, n)=1, then m + n is equal to

1. 22
2. 31
3. 13
4. 9

Correct answer: 22

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