3L 3E Solution
Let A be the initial point of the given ray.
- Construct a circle C1 with center A and an arbitrary radius, intersecting the ray at B
- Construct the circle C2 with center B and radius AB, intersecting circle C1 at C and D
- Construct line AC
- Construct line AD
All internal angles of an equilateral triangle are 60°, so you just need to construct the two sides of an equilateral triangle adjacent to vertex A.
The two circles ensure that AB=AC=BC and AB=AD=BD and so ABC and ABD are equilateral and angles CAB and DAB are 60°.
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