1998 AMC 12 Problem 11
Attempt Problem 11 of the 1998 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 1998 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
11.
Let be a rectangle. How many circles in the plane of have a diameter both of whose endpoints are vertices of
Answer: D
Small hint:
There are six unordered pairs of rectangle vertices
Big hint:
The two diagonals determine the same circle
Solution:
The four sides determine four distinct diameter circles. The two diagonals are equal and share a midpoint, so they determine the same fifth circle. Hence there are and D is correct.
Problem 11 in other years
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