I will post problems here when I feel like it.
Problem 1. Source: aops
A square and equilateral triangle are circumscribed around a common circle. What is the ratio of their areas?
Jew! Wait...
Since the triangle is equilateral, the center of the circle is not only the incenter but the centroid. Therefore, the height of the triangle is in a 3:1 ratio with the radius of the circle. Assuming a unit circle, the height is 3, and the area is 3*sqrt(3). The square's area is 1.
Triangle:Square = 3sqrt(3)/4.
[Edit]: Haha fuck, the squares area is 4, lulz.
Quote from: Deuce on February 27, 2008, 09:13:00 PM
Since the triangle is equilateral, the center of the circle is not only the incenter but the centroid. Therefore, the height of the triangle is in a 3:1 ratio with the radius of the circle. Assuming a unit circle, the height is 3, and the area is 3*sqrt(3). The square's area is 1.
Triangle:Square = 3sqrt(3)/4.
[Edit]: Haha fuck, the squares area is 4, lulz.
Correct!