Regular Polygons Inscribed in a Circle Practice Test

When constructing a regular octagon inscribed in a circle, a student first constructs perpendicular diameters to create four equally spaced points. What construction technique should be applied next to locate the remaining four vertices?

In constructing a regular dodecagon (12-sided polygon) inscribed in a circle, a student plans to use the relationship between a dodecagon and simpler regular polygons. Which combination of constructions would most efficiently create the 12 equally-spaced vertices?