2010 AMC 8 Problems/Problem 19
Contents
Problem
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?
Solution
Since is isosceles, bisects . Thus . From the Pythagorean Theorem, . Thus the area between the two circles is
Note: The length is necessary information, as this tells us the radius of the larger circle. The area of the annulus is .
Video Solution
https://youtu.be/Q6rnoQChiyU. Soo, DRMS, NM
Video Solution by OmegaLearn
https://youtu.be/51K3uCzntWs?t=3206
~ pi_is_3.14
Video by MathTalks
https://www.youtube.com/watch?v=KSYVsSJDX-0&feature=youtu.be
See Also
2010 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.