triangle/circle thing

Probe · May 23, 2006, 03:56 PM

you have a circle with a radius of 1 inscribed in a general triangle. what is the minimum area of the triangle? anyone know how to do this or could give some hints?

rabbit · May 23, 2006, 04:03 PM

The minimum area of the triangle is slightly more than that of the circle

Probe · May 23, 2006, 04:04 PM

thanks, but that doesnt really help =]

rabbit · May 23, 2006, 05:25 PM

Then you, sir, have asked the wrong questions, because my post is exactly what you asked for.

Probe · May 23, 2006, 05:44 PM

Quote from: rabbit on May 23, 2006, 05:25 PM
Then you, sir, have asked the wrong questions, because my post is exactly what you asked for.

well sorry for not stating it explicitly, but i assumed people would know what i meant. let me rephrase for those who cant understand then:
could anyone explain, or give a hint, how to solve this, how to find the area of the triangle, given only the radius of the inscribed circle?

Explicit · May 23, 2006, 06:13 PM

Quote from: Probe on May 23, 2006, 03:56 PM
you have a circle with a radius of 1 inscribed in a general triangle. what is the minimum area of the triangle? anyone know how to do this or could give some hints?

Find the area of the triangle, then subtract the circle's area from the triangle's area to find what I think would be the minimum area of the triangle.

Probe · May 23, 2006, 06:23 PM

Quote from: Explicit[nK] on May 23, 2006, 06:13 PM
Quote from: Probe on May 23, 2006, 03:56 PM
you have a circle with a radius of 1 inscribed in a general triangle. what is the minimum area of the triangle? anyone know how to do this or could give some hints?

Find the area of the triangle, then subtract the circle's area from the triangle's area to find what I think would be the minimum area of the triangle.

thanks, but how do i find the area of the triangle if all i know is the radius of the circle?

Lenny · May 23, 2006, 08:21 PM

You'll find some who don't know the answer (or even the question) post things which aren't worth reading on these forums

Regardless....

The inscribed triangle will have to be equilateral to minimize the area. IIRC, there is another area formula specifically for an equilateral triangle.

But there is some identity relationship between the equilateral (or general) triangle and the circle I'm missing...

Using this identity, you could probably make a formula for the area, differentiate it and set this equal to 0 to find the minimum...

FrOzeN · May 23, 2006, 10:47 PM

http://mathworld.wolfram.com/EquilateralTriangle.html

This looks useful to what your after.