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…

Question

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

MARKS Content Team · Accepted Answer

Correct answer: (B) 1/4. 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^2-2y+1=r^2+2r+1 ⇒1+r^2-2r=r^2+2r, ∵ y=r ∴1=4r ∴ r=1/4

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

Solution

Relevant Questions