1975 AMC 12 Problem 28
Attempt Problem 28 of the 1975 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 1975 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
28.
In triangle shown in the adjoining figure, is the midpoint of side and Points and are taken on and respectively, and lines and intersect at If then equals
not enough information given to solve the problem
Answer: A
Small Hint:
Represent by vectors from
Big Hint:
If then equate the coefficients of a point on and on
Solution:
Put at the origin and write the position vectors of as If then and so Write Because also lies on the median its and coefficients are equal: Hence Along and so
Therefore, the correct answer is A.
Problem 28 in Other Years
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