If I have an equilateral triangle with sides of 4", how do I figure out what the diameter of a circle would be that touches the three points?

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- Dec 16th 2012, 08:36 PMJambeDiameter of circle--equilateral triangle
If I have an equilateral triangle with sides of 4", how do I figure out what the diameter of a circle would be that touches the three points?

- Dec 16th 2012, 09:21 PMphys251Re: Diameter of circle--equilateral triangle
Draw it out; make sure the diagram isn't too small. Write EVERYTHING you know about the circle and the triangles (notice I said triangle

**s**--there's a hint). - Dec 17th 2012, 08:42 AMJambeRe: Diameter of circle--equilateral triangle
I should have said that this is not homework. I am 71 years old. If I had a compass I would try to figure it out geometrically as follows:

Bisect a side, set the compass to one half the side, draw an arc. Do the same thing with an adjacent--oops, that's not going to work. I would have to have the circle which is what I am trying to find.

Well, I've read some similar discussions (below) and apparently this can't be solved just using geometry--you have to use Pythagorean theorem to solve for r. Thanks anyway. - Dec 17th 2012, 09:00 AMMarkFLRe: Diameter of circle--equilateral triangle
If we deconstruct the equilateral triangle into 3 congruent isosceles 30°-30°-120° triangles, we find the two equal sides of these isosceles triangles is the radius of the circle.

Then, we may find the radius*r*in inches is:

$\displaystyle r=2\sec(30^{\circ})=\frac{4}{\sqrt{3}}$

And so the diameter*d*is:

$\displaystyle d=2r=\frac{8}{\sqrt{3}}\approx4.62\text{ in}$. - Dec 17th 2012, 09:02 AMPlatoRe: Diameter of circle--equilateral triangle

This page answers your question.

You want the radius of the inscribed circle. It is right there. - Dec 17th 2012, 09:53 AMJambeRe: Diameter of circle--equilateral triangle
- Dec 17th 2012, 12:19 PMPlatoRe: Diameter of circle--equilateral triangle