grandh01 wrote:If P and Q are points in a plane and P lies inside the circle C with
center O and radius 2, does Q lie inside circle C?
(1) The length of line segment OP is 1.
(2) OPQ is an equilateral triangle.
oa is b
Given:
- Circle with center O and radius = 2.
- Point P is inside the circle
IMPORTANT: If Point P is inside the circle then the line segment OP must be less than 2 (the radius of the circle)
Target question: Is Point Q in the circle?
Statement 1: The length of line segment OP is 1.
This tells us nothing about Point Q, so there's no way to answer the
target question with any certainty.
So, statement 1 is NOT SUFFICIENT
Statement 2: OPQ is an equilateral triangle.
In an equilateral triangle, the lengths of all three sides are equal. In other words, OP=OQ=PQ
This is useful because point O is at the circle's center.
We already concluded (above) that the length of OP is less than 2. This means that the length of OQ is also less than 2.
If the length of OQ is less than 2, then
Point Q must lie inside the circle.
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer =
B
Cheers,
Brent
