The tangent to the circle C1 : x2 + y2 - 2x - 1 = 0 at the point (2, 1) cuts off a chord of length 4 from a circle C2 whose center is (3, -2). The radius of C2 is :

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Answer: D. \sqrt 6 Here, equation of tangent on C1 at (2, 1) is : 2x + y - (x + 2) -1 = 0 Or x + y = 3 If it cuts off the chord of the circle C2 then the equation of the chord is : x + y = 3 	herefore\,\,\, distance of the chord from (3, - 2) is : d = \left| {{{3 - 2 - 3} \over {\sqrt 2 }}} ight| = \sqrt 2 Also, length of the chord is l = 4 	herefore\,\,\, radius of C2 = r = \sqrt {{{\left( {{l \over 2}} ight)}^2} + {d^2}} = \sqrt {{{\left( 2 ight)}^2} + {{\left( {\sqrt 2 } ight)}^2}} = \sqrt 6

The tangent to the circle C1 : x2 + y2 $$-$$ 2x $$-$$ 1 = 0 at the point (2, 1) cuts off a chord of length 4 from a circle C2 whose center is (3, $$-$$2). The radius of C2 is :

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