Question

When constructing an inscribed equilateral triangle, how many arcs will be drawn on the circle?

Answer 1

The answer is A(3). 3 arcs will be drawn

Answer 2

It can be done with 2 arcs. In the attached, I started with diameter AD, then drew arcs at B and C of the same radius as the circle from a center at A. Triangle BCD is the inscribed equilateral triangle.

Perhaps a more usual method would be to start at D, draw an arc at E, then from there at B. Resetting the compass to have radius, DB, a third arc can be drawn at C using either B or D as the center. This method would give you
.. selection A: 3 arcs

If you didn't want to reset the compass, you could draw two more arcs, say from B to A, then from A to C. This method would give you
.. selection B: 4 arcs.