Hi All,
We're asked if the point Q is on the circle with center C. This is a YES/NO question and can be approached with some logic (and a few examples/drawings might help).
(1) R is a point on the circle and the distance from Q to R is equal to the distance from Q to C.
Since C is the CENTER of the circle, and R is on the circumference, we know that CR is a RADIUS of the circle. With the information in Fact 1, point Q can be ANY point that is equidistance from R and C.
IF....
-we have an equilateral triangle, with R and Q on the circumference, then the answer to the question is YES.
-we have point Q in the exact middle of the radius CR, then the answer to the question is NO.
Fact 1 is INSUFFICIENT
(2) S is a point on the circle and the distance from Q to S is equal to the distance from S to C.
Since C is the CENTER of the circle, and S is on the circumference, we know that CS is a RADIUS of the circle. With the information in Fact 2, we know that the length of QS is the SAME length as the RADIUS.
IF....
-we have an equilateral triangle, with S and Q on the circumference, then the answer to the question is YES.
-we have point Q in any other position that is exactly one radius in length from point S, then the answer to the question is NO.
Fact 2 is INSUFFICIENT
Combined, we know...
R is a point on the circle and the distance from Q to R is equal to the distance from Q to C.
S is a point on the circle and the distance from Q to S is equal to the distance from S to C.
With both Facts, we can create two different examples:
-we have two equilateral triangles, with Q on the circumference and R and S on opposite sides of Q, then the answer to the question is YES.
-we have an isosceles triangle, with Q OUTSIDE of the circle and CR as the non-equal side, then the answer to the question is NO.
Combined, INSUFFICIENT
Final Answer:
GMAT assassins aren't born, they're made,
Rich
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