Problems

[Ender]

I will post problems here when I feel like it.

[Ender]

Problem 1. Source: aops

A square and equilateral triangle are circumscribed around a common circle. What is the ratio of their areas?

[rabbit]

Jew!  Wait...

[d&q]

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.

[Ender]

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!