1967 AMC 12 Problem 29
Attempt Problem 29 of the 1967 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 1967 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
29.
is a diameter of a circle. Tangents and are drawn so that and intersect in a point on the circle. If and the diameter of the circle is:
Answer: C
Small hint:
Let the intersection point on the circle be ; then
Big hint:
Use the parallel tangents to compare right triangles and
Solution:
Let be the diameter. Since the intersection of and lies on the circle, those two lines are perpendicular by Thales’ theorem. Also the tangents and are parallel. The resulting right triangles and are similar, so Hence and
Therefore, the correct answer is C.
Problem 29 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
- 1953 AMC 12
- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
- 1957 AMC 12
- 1958 AMC 12
- 1959 AMC 12
- 1960 AMC 12
- 1961 AMC 12
- 1962 AMC 12
- 1963 AMC 12
- 1964 AMC 12
- 1965 AMC 12
- 1966 AMC 12
- 1968 AMC 12
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- 1972 AMC 12
- 1973 AMC 12
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- 1976 AMC 12
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- 1981 AMC 12
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- 1984 AMC 12
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- 1989 AMC 12
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- 1991 AMC 12
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- 1995 AMC 12
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- 1997 AMC 12
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- 1999 AMC 12