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?
1. **Initial Setup**: We start with a circle centered at point \( O \) and a known point \( P \) on the circle.

2. **First Move**: Draw a line through the known point \( P \) and the center \( O \). This line will intersect the circle at another point, which we will call \( X \). Now, \( X \) is a known point.

3. **Second Move**: Draw a circle centered at \( X \) with radius \( XO \). This circle will intersect the original circle at two points. Let's call these points \( A \) and \( B \). Now, \( A \) and \( B \) are known points.

4. **Third Move**: Draw a line through points \( A \) and \( B \). This line will intersect the original circle at two points, which we will call \( C \) and \( D \). Now, \( C \) and \( D \) are known points.

5. **Fourth Move**: Draw a circle centered at \( C \) with radius \( CO \). This circle will intersect the original circle at two points. Let's call these points \( E \) and \( F \). Now, \( E \) and \( F \) are known points.

6. **Fifth Move**: Draw a line through points \( E \) and \( F \). This line will intersect the original circle at two points, which we will call \( G \) and \( H \). Now, \( G \) and \( H \) are known points.

By following these steps, we have constructed an equilateral triangle inscribed in the original circle using the minimum number of moves.

The final answer is \(\boxed{5}\).