1978 AHSME Problems/Problem 10

Revision as of 11:16, 13 February 2021 by Coolmath34 (talk | contribs) (Created page with "== Problem 10 == If <math>\mathit{B}</math> is a point on circle <math>\mathit{C}</math> with center <math>\mathit{P}</math>, then the set of all points <math>\mathit{A}</mat...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem 10

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

$\textbf{(A) }\text{the line segment from }P \text{ to }B\qquad\\ \textbf{(B) }\text{the ray beginning at }P \text{ and passing through }B\qquad\\ \textbf{(C) }\text{a ray beginning at }B\qquad\\ \textbf{(D) }\text{a circle whose center is }P\qquad\\ \textbf{(E) }\text{a circle whose center is }B$


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


See Also

1978 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 9
Followed by
Problem 11
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
All AHSME Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png