1990 AMC 12 Problem 6
Attempt Problem 6 of the 1990 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 1990 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
6.
Points and are units apart. How many lines in a given plane containing and are units from and units from
more than
Answer: D
Small hint:
Replace the distance conditions by tangencies to two circles
Big hint:
The circles have radii and and are externally tangent
Solution:
A qualifying line is a common tangent to the circle centered at with radius and the circle centered at with radius Their center distance equals the sum of their radii, so they are externally tangent. They have two external common tangents and one common tangent at their point of contact, for a total of
Thus the correct answer is D.
Problem 6 in other years
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