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

Step-by-step solution

Here, equation of tangent on C₁ at (2,1) is: 2 x+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 distance of the chord from (3,-2) is : d= | 3-2-3 2 |= 2 Also, length of the chord is l=4 aligned radius of C₂=r &= ( l 2 )^2+d^2 &= (2)^2+( 2 )^2 = 6 aligned