Difference between revisions of "2005 AMC 10B Problems/Problem 7"
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Revision as of 20:48, 11 April 2013
Problem
A circle is inscribed in a square, then a square is inscribed in this circle, and finally, a circle is inscribed in this square. What is the ratio of the area of the smaller circle to the area of the larger square?
Solution
Let the side of the largest square be . It follows that the diameter of the inscribed circle is also . Therefore, the diagonal of the square inscribed inscribed in the circle is . The side length of the smaller square is . Similarly, the diameter of the smaller inscribed circle is . Hence, its radius is . The area of this circle is , and the area of the largest square is . The ratio of the areas is .
See Also
2005 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
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 AMC 10 Problems and Solutions |