The tangent to the circle C1: x² + y² - 6x - 5 = 0 at the point (2, 1) cuts off a chord of length 4 from a circle C2 whose centre is (3, -6). The radius of C2 is

Equation of tangent on C1 at (2, 1) is: 2x + y - (x + 2)5 = 0
x + y = 3
If it cuts off the chord of the circle C2 then the equation of the chord is: x + y = 3
Distance of the chord from (3, -6) d = √(3 - 6)/√2 = √2
Length of the chord is l = 4
r² = l²/4 + d² where r is the radius of the circle.
r² = 4 + 2 = 6
⇒ r = √6