1960 AMC 12 Problem 12
Attempt Problem 12 of the 1960 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1960 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
12.
The locus of the centers of all circles of given radius in the same plane, passing through a fixed point, is:
a point
a straight line
two straight lines
a circle
two circles
Answer: D
Small hint:
Every center must be exactly one radius from the fixed point
Big hint:
Identify the locus of points at a fixed positive distance from one point
Solution:
A circle of radius passes through the fixed point exactly when its center is distance from that point. The locus of all such centers is a circle of radius
Therefore, the correct answer is D.
Problem 12 in other years
- 1950 AMC 12
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