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If I have a circle inscribed inside an equilateral triangle, and I know the radius of the circle, what is the formula to determine what the length of the side of the triangle is?

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4 Answers 4

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The Wikipedia page one equilateral triangles gives the radius of the inscribed circle as $r=a\frac{\sqrt{3}}{6}$ where $a$ is the side. So $a=r\frac{6}{\sqrt{3}}$.

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or equivalently $a=2{\sqrt{3}}r$ –  Chris Card Jan 25 '11 at 17:43

It would be $\tan 30^{\circ} = \frac{r}{x}$ so that $x = \frac{r}{\tan 30^{\circ}}$ where $x$ is half of a side.

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if only radius of the circle is known in inscribed circle then you can find the length of all the sides cos30=x/r or sine60=x/renter image description here

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the answer is because you must first divide the triangle into 6 right triangles and then using a^2 + b^2 =c^2 figure out the area of the right triangle then again multiply by three. I got (3√3/4)

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