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The line L 1 ≡ 3 x - 4 y + 1 = 0 touches the circles C 1 and C 2 . Centers of C 1 and C 2 are A 1 ( 1,2 ) and A 2 3 , 1 respectively Then, the length (in units) of the transverse common tangent of C 1 and C 2 is equal to

Correct answer

1

Step-by-step solution

Note that A 1 and A 2 lie on different sides of L 1 , hence L 1 is a transverse common tangent Radius of C 1 = 3 - 8 + 1 5 = 4 5 Radius of C 2 = 9 - 4 + 1 5 = 6 5 A 1 A 2 = 4 + 1 = 5 ⇒ Length of the transverse common tangent is A 1 A 2 2 - r 1 + r 2 2 = 5 - 2 2 = 1 unit

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