1957 AMC 12 Problem 34
Attempt Problem 34 of the 1957 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 1957 AMC 12 solutions, or check the answer key.
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34.
The points that satisfy the system where the symbol “” means “less than,” constitute the following set:
only two points
an arc of a circle
a straight line segment not including the
end-points
a straight line segment including the end-points
a single point
Answer: C
Small hint:
Interpret as the interior of a circle
Big hint:
Intersect that open disk with the line
Solution:
The inequality describes the open disk inside the circle of radius centered at the origin. The line crosses the circle in two points. Its portion inside the disk is the segment between those points, but the strict inequality excludes the endpoints.
Thus, the correct answer is C.