Competition problem — Geometry — Maths Olympiad Prep

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Geometry Difficulty 2.7 Junior Find the answer

If $\mathit{B}$ is a point on circle $\mathit{C}$ with center $\mathit{P}$ , then the set of all points $\mathit{A}$ in the plane of circle $\mathit{C}$ such that the distance between $\mathit{A}$ and $\mathit{B}$ is less than or equal to the distance between $\mathit{A}$
and any other point on circle $\mathit{C}$ is

Pick one

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 $\boxed{\textbf{(B)}}.$

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.