## Circumscribed Triangle

#### Problem

An equilateral triangle is circumscribed.

Find the area of the triangle.

#### Solution

Consider the following diagram.

Using the Pythagorean Theorem, 4`x`^{2} = `x`^{2} + 9

3`x`^{2} = 9 `x` = 3.

Area of triangle is 33.

It can be seen that the perimeter of the triangle is 63, i.e. double the area. What radius circle would have a circumscribed equilateral triangle with an area the same size as the perimeter?

Problem ID: 108 (Mar 2003) Difficulty: 2 Star