2010 AMC 8 Problem 19
Attempt Problem 19 of the 2010 AMC 8 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 2010 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
19.
The two circles pictured have the same center Chord is tangent to the inner circle at is and chord has length What is the area between the two circles?
Answer: C
Small hint:
Half the chord, the inner radius, and the outer radius form a right triangle.
Big hint:
The radius to a tangent point is perpendicular to the chord.
Solution:
The area between the two circles is the area of the larger circle minus the area of the smaller circle. This would be By the Pythagorean Theorem, we can get Therefore, we need to find
Since is half of we get This makes
Thus, the answer is C .
Problem 19 in other years
- 1985 AMC 8
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