1953 AMC 12 Problem 42
Attempt Problem 42 of the 1953 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 1953 AMC 12 solutions, or check the answer key.
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42.
The centers of two circles are inches apart. The smaller circle has a radius of inches and the larger one has a radius of inches. The length of the common internal tangent is:
inches
inches
inches
inches
inches
Answer: E
Small hint:
For an internal common tangent, the perpendicular separation of the centers from the tangent is the sum of the radii
Big hint:
Use a right triangle with hypotenuse and one leg
Solution:
The center segment, the tangent segment, and a perpendicular leg of length form a right triangle. Thus the tangent length is inches.
Thus, the correct answer is E.