Anita plays the following single-player game: She is given a circle in the plane. The center of this circle and some point on the circle are designated “known points”. Now she makes a series of moves, each of which takes one of the following forms:
(i) She draws a line (infinite in both directions) between two “known points”; or
(ii) She draws a circle whose center is a “known point” and which intersects another “known point”.
Once she makes a move, all intersections between her new line/circle and existing lines/circles become “known points”, unless the new/line circle is identical to an existing one. In other words, Anita is making a ruler-and-compass construction, starting from a circle.
What is the smallest number of moves that Anita can use to construct a drawing containing an equilateral triangle inscribed in the original circle?