1960 AMC 12 Problem 6

Attempt Problem 6 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).

6.

The circumference of a circle is 100100 inches. The side of a square inscribed in this circle, expressed in inches, is:
252π\dfrac{25\sqrt2}{\pi}
502π\dfrac{50\sqrt2}{\pi}
100π\dfrac{100}{\pi}
1002π\dfrac{100\sqrt2}{\pi}
50250\sqrt2
Answer: B
Concepts:circumferencesquare (geometry)diagonal
Small hint:
Find the diameter from the circumference
Big hint:
The diagonal of the inscribed square is the circle’s diameter
Solution:
The diameter is 100π.\frac{100}{\pi}. If the square has side s,s, its diagonal is s2,s\sqrt2, so s2=100π. s\sqrt2=\frac{100}{\pi}. Therefore s=502π.s=\frac{50\sqrt2}{\pi}.
Thus, the correct answer is B.
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