1995 AMC 12 Problem 28
Attempt Problem 28 of the 1995 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 1995 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
28.
Two parallel chords in a circle have lengths and and the distance between them is The chord parallel to these chords and midway between them is of length where is
Answer: E
Small hint:
If a chord is at signed distance from the center, its half-length satisfies
Big hint:
Let the signed distances of the - and -chords differ by , and subtract their equations
Solution:
Let the signed distances from the center to the - and -chords be and with Then Hence so Since we get and therefore and The midway chord is at signed distance while Its squared length is so Thus the correct answer is E.
Problem 28 in other years
- 1950 AMC 12
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