Posted by **Ngoc** on Tuesday, January 11, 2011 at 8:16pm.

How do you find the distance from the center of an equilateral triangle, with the side length of L, to a point?

- Geometry -
**Reiny**, Tuesday, January 11, 2011 at 8:24pm
The centre of an equilateral triangle is the centroid of the triangle.

That centroid is 2/3 of the length of the median away from a vertex.

So we need the length of a median.

Drawing one median in an equilateral triangle results in right angled triangle with angles 30-60-90, and you should know that the sides of that triangle are in the ratio of 1:√3:2

So if the hypotenuse is L, then

median/L = √3/1

median = √3 L

so the distance from the ''centre" to the vertex is

(2/3)(√3 L) = 2L√3/3

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