1986 AMC 12 Problem 27
Attempt Problem 27 of the 1986 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 1986 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
27.
In the adjoining figure, is a diameter of the circle, is a chord parallel to and intersects at with The ratio of the area of to that of is
Answer: C
Small hint:
Express each triangle’s area using the two sides meeting at
Big hint:
Use the intersecting-chords theorem, then draw and use the right triangle created by diameter
Solution:
The triangles use the same angle at so Intersecting chords give so this ratio becomes Draw Since is a diameter, and are collinear. Thus triangle is right at and The required ratio is
Thus the correct answer is C.
Problem 27 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
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- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
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