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smc

geometry intermediate

Problem

If is a point on circle with center , then the set of all points in the plane of circle such that the distance between and is less than or equal to the distance between and any other point on circle is
(A)
(B)
(C)
(D)
Solution
Begin by drawing circle P and point B. To satisfy the conditions of the problem, A needs to be in a position where it is closer to B. This can only happen if A and B are on the same line, so we choose from answer choices A and B. We can pick some arbitrary point A outside circle P that is collinear with B and see that the conditions still hold, so the answer is
Final answer
B