1991 AMC 12 Problem 4
Attempt Problem 4 of the 1991 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 1991 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
4.
Which of the following triangles cannot exist?
An acute isosceles triangle
An isosceles right triangle
An obtuse right triangle
A scalene right triangle
A scalene obtuse triangle
Answer: C
Small hint:
A right triangle already contains an angle of
Big hint:
An obtuse triangle must contain an angle greater than
Solution:
A right triangle has one angle, leaving only for its other two positive angles together. Neither remaining angle can therefore be obtuse. Hence a triangle cannot be both right and obtuse.
Thus the correct answer is C.
Problem 4 in other years
- 1950 AMC 12
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