1959 AMC 12 Problem 26
Attempt Problem 26 of the 1959 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 1959 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
26.
The base of an isosceles triangle is The medians to the legs intersect each other at right angles. The area of the triangle is:
Answer: A
Small hint:
Place the base endpoints symmetrically about the origin and the third vertex on the perpendicular bisector
Big hint:
Write direction vectors for the two medians and set their dot product equal to zero
Solution:
Put the base endpoints at and and let the third vertex be The median from has direction while the median from has direction Their dot product is zero, so and Thus the area is
Therefore, the correct answer is A.
Problem 26 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
- 1953 AMC 12
- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
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