Let C be the circle with center at 1 , 1 and radius = 1 . If T is the circle centered at 0 , y , passing through the origin and touching the circle C externally, then the radius of T is equal to

Step-by-step solution

Let r be the required radius As origin lies on the circle, the distance of 0 , 0 from 0 , y = r ∴  y = r As the two circles touch externally, distance between centres is sum of the radii ⇒ 0 - 1 2 + y - 1 2 = r + 1 ⇒ 1 + y 2 - 2 y + 1 = r 2 + 2 r + 1 ⇒ 1 + r 2 - 2 r = r 2 + 2 r , ∵    y = r ∴ 1 = 4 r ∴     r = 1 4