1957 AMC 12 Problem 48
Attempt Problem 48 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.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
48.
Let be an equilateral triangle inscribed in circle is a point on arc Lines and are drawn. Then is:
equal to
less than
greater than
equal to, less than, or greater than depending upon
the position of
none of these
Answer: A
Small hint:
Apply Ptolemy’s theorem to cyclic quadrilateral
Big hint:
Use to cancel the common side length
Solution:
In cyclic quadrilateral Ptolemy’s theorem gives Since is equilateral, Dividing by this common length yields
Therefore, the correct answer is A.