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
(B)
See also
1966 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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