1972 AMC 12 Problem 18
Attempt Problem 18 of the 1972 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 1972 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
18.
Let be a trapezoid with the measure of base twice that of base and let be the point of intersection of the diagonals. If the measure of diagonal is then that of segment is equal to:
Answer: A
Small hint:
Triangles and are similar
Big hint:
The base ratio also equals
Solution:
Since triangles and are similar. Hence Thus so
Therefore, the correct answer is A.
Problem 18 in other years
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