1978 AHSME Problems/Problem 10
Problem 10
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
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
See Also
1978 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
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