A circle C of radius 2 lies in the second quadrant and touches both the coordinate axes. Let r be the radius of a circle that has centre at the point ( 2 , 5 ) and intersects the circle C at exactly t

Question

A circle C of radius 2 lies in the second quadrant and touches both the coordinate axes. Let r be the radius of a circle that has centre at the point ( 2 , 5 ) and intersects the circle C at exactly two points. If the set of all possible values of r is the interval ( α , β ) , then 3 β − 2 α is equal to :

TestHub · Accepted Answer

C 1 C 2 = ( 2 + 2 ) 2 + ( 5 − 2 ) 2 = 16 + 9 = 5 r + 2 > 5 r > 3 r < 5 + 2 r < 7 ∴ α = 3 , β = 7 3 β − 2 α = 3 ( 7 ) − 2 ( 3 ) = 21 − 6 = 15

Mathematics - Circle Question with Solution | TestHub

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