Clan x86

General Forums => Academic / School => Math and Other Problems => Topic started by: Ender on February 27, 2008, 06:21:19 am

Title: Problems
Post by: Ender on February 27, 2008, 06:21:19 am

I will post problems here when I feel like it.

Title: Re: Problems
Post by: Ender on February 27, 2008, 06:24:39 am

Problem 1. Source: aops

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

Title: Re: Problems
Post by: rabbit on February 27, 2008, 08:09:32 am

Jew!  Wait...

Title: Re: Problems
Post by: d&q 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.

Title: Re: Problems
Post by: Ender on February 28, 2008, 03:41:30 am

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!