2019 AMC 12B Problem 11
Attempt Problem 11 of the 2019 AMC 12B 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 2019 AMC 12B solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
11.
How many unordered pairs of edges of a given cube determine a plane?
Answer: D
Small hint:
Two edges determine a plane unless they are skew
Big hint:
Count the pairs that are parallel and the pairs that share a vertex
Solution:
Two edges determine a plane exactly when they are coplanar, that is, parallel or intersecting.
The edges split into directions of parallel edges, giving parallel pairs. Edges sharing a vertex give intersecting pairs.
The total is
Thus, D is the correct answer.
Problem 11 in other years
- 1950 AMC 12
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