Y inside the same

[sanju09]

If point X is inside a circle with center O and radius 2, is point Y inside the same circle?

(1) OX = 1.

(2) XY = 2.5.


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[Rich@VeritasPrep]

If point X is inside a circle with center O and radius 2, is point Y inside the same circle?

(1) OX = 1.

Nothing about Y. INSUFFICIENT

(2) XY = 2.5.

Diameter of the circle is 4, so XY could be entirely within the circle, in which case Y would be inside the circle.

However, XY could be a line segment with X inside the circle and Y outside the circle. INSUFFICIENT

Together, we know OX=1 and XY=2.5. So consider these two situations:

1. O is between X and Y. In that case, OY=1.5. That is smaller than the radius, so Y would be inside the circle

2. X is between O and Y. In that case, OY =3.5. That is larger than the radius so Y would be outside the circle.

INSUFFICIENT

Ans: E

[niksworth]

IMO E

Statement 1 gives only info about point X, so alone, it is insufficient.

Statement 2 gives XY = 2.5. Now the diameter of the circle is 4, so Y can lie either inside or outside the circle depending on the relative positions of X and Y. Thus Statement 2 alone is insufficient.

Bringing 1 and 2 together, if OX = 1 and XY = 2.5, Y can have any position depending on angle OXY. If OXY is 180 deg, then Y lies outside the circle. If angle OXY is 0 deg, then Y lies inside the circle. Thus statements 1 and 2 together are also not sufficient.

Hence the answer should be E.