1966 AHSME Problems/Problem 4
Problem
Circle I is circumscribed about a given square and circle II is inscribed in the given square. If is the ratio of the area of circle I to that of circle II, then equals:
Solution
Make half of the square's side . Now the radius of the smaller circle is , so it's area is . Now find the diameter of the bigger circle. Since half of the square's side is , the full side is . Using the Pythagorean theorem, you get the diagonal to be . Half of that is the radius, or . Using the same equation as before, you get the area of the larger circle to be . Putting one over the other and dividing, you get two as the answer: or .
See also
1966 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.