1952 AMC 12 Problem 29
Attempt Problem 29 of the 1952 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 1952 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
29.
In a circle of radius units, and are perpendicular diameters. A chord cutting at is units long. The diameter is divided into two segments whose dimensions are:
None of these
Answer: A
Small hint:
Put the center at the origin, take , and represent the other endpoint of the chord by coordinates
Big hint:
Use and , then find where line crosses the horizontal diameter
Solution:
Put the circle at the origin with and let The equations give and Taking does not change the segment lengths.
The line from to crosses at Its distances to the endpoints and of diameter are therefore
Thus, the correct answer is A.
Problem 29 in other years
- 1950 AMC 12
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- 1953 AMC 12
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