Consider a circle C which touches the y - axis at 0 , 6 and cuts off an intercept 6 5 on the x - axis. Then the radius of the circle C is equal to :

Step-by-step solution

We have, a circle C which touches the y - axis at 0 , 6 and cuts off an intercept 6 5 on the x - axis. We know that, length of the chord of the circle using perpendicular distance from the center is 2 r 2 - d 2 where r is the radius of the circle and d is the perpendicular distance from the center to the chord. From the given data, we have the following diagram Hence, length of the chord of the circle ⇒ 2 r 2 - d 2 = 6 5 ⇒ r 2 - d 2 = 3 5 On squaring on both sides ⇒ r 2 - d 2 = 45 ⇒ d 2 = r