1. NS .
2. NS .

Together: Under the given conditions any circle with r>2.5 & in which A is given to be inside & where OB =2.5 & AB=5, Both the pts A & B will lie inside the circle.

Hence C.

Hope i am not missing anything.

gvosough wrote:line segment AB lies in a plane & has a length of 5. If A lies inside circle x with centre O, does B lie inside circle X?
1) the radius of circle X is 4
2) the length of line segment BO is 2.5

Oa:b[/spoiler]

I went with C initially but let's see how the answer is B.

So the best chance of getting B inside the circle is by coinciding segment AB with the diameter on the circle (maximum length that can fit inside the circle). So now if line segment AB coincides with diameter of circle, and AB is 5 and OB is 2.5 that means circle center O has to be the midpoint of line segment AB. That means point A is on one end of diameter and point B on the other. OB will be greater than 2.5 if B is outside of the circle. I am not sure if this is the best way to derive it. May be experts can show a more conclusive approach.

DarkKnight wrote:I went with C initially but let's see how the answer is B.

So the best chance of getting B inside the circle is by coinciding segment AB with the diameter on the circle (maximum length that can fit inside the circle). So now if line segment AB coincides with diameter of circle, and AB is 5 and OB is 2.5 that means circle center O has to be the midpoint of line segment AB. That means point A is on one end of diameter and point B on the other. OB will be greater than 2.5 if B is outside of the circle. I am not sure if this is the best way to derive it. May be experts can show a more conclusive approach.

Agree with u DarkKnight. So Trying to see it more clearly.

2) If OB =2.5, If B is outside the circle , A cant be inside the circle as AB has to be 5. This violates the condition given in the question . Not possible.

--> If OB =2.5 & B is inside the circle , A has to be inside the circle. Satisfies the condition.So Sufficient.

Kind of Reverse Approach.

IMO B