One Construction to Rule Them All

Draw a horizontal segment as the base. Using each endpoint as a center and the segment length as radius, draw two circles that intersect at two points, one above and one below. Connect these two intersection points with a vertical line, which crosses the base at its midpoint. Then draw two segments from the left endpoint to the midpoint and from the midpoint to the right endpoint. Finally, mark the angle formed at the midpoint between the right endpoint and the upper intersection point. The figure shows symmetric circles, a vertical line, and a triangle-like arrangement.