(adsbygoogle = window.adsbygoogle || []).push({}); 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.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

**Physics Forums | Science Articles, Homework Help, Discussion**