# Homework Help: Minimum area of a triangle with fixed incircle

1. May 4, 2010

### Referos

1. The problem statement, all variables and given/known data
Consider an isosceles triangles with height x and a fixed incircle of radius R. Show that the minimum area of such triangle occurs when x = 3R

2. Relevant equations
None.

3. The attempt at a solution
Well, I know that have to express the area of the triangle in terms of x, then differentiate with respect to x and find where the derivative is zero, and then check whether it's a minimum or maximum. My problem is mostly with the geometric part of the problem. Since I have the height x, I suppose that I need to find the base in terms of x, since area = 1/2 * base * height.
The only thing I've managed to do is drawing a line from the center of the incircle to one of the points of tangent; this gives a right triangle with a cathetus equal to R and a hyponetuse equal to x - R. I've tried finding similar triangles but it didn't work so well.
Thanks.

2. May 5, 2010