Equilateral Triangle

Inscribed in a Circle
1. Begin with a circle centered on O and a point A on it.

2. Construct the circle $$\overset{\frown} {A O}$$. It intersects $$\overset{\frown} {O A}$$ at points B and C.

3. Construct the circles $$\overset{\frown} {B O}$$ and $$\overset{\frown} {C O}$$. They intersect $$\overset{\frown} {O A}$$ at points D and E.

4. Construct the line segments $$\overline{A D}$$, $$\overline{A E}$$ and $$\overline{D E}$$.

From a Given Side Length
1. Begin with a line segment $$\overline{A B}$$ of a given length.

2. Construct two circles $$\overset{\frown} {A B}$$ and $$\overset{\frown} {B A}$$. They intersect at point C.

3. Construct line segments $$\overline{A C}$$ and $$\overline{B C}$$.