Ethan is likely in the process of constructing a regular pentagon. When inscribing a polygon in a circle using a compass and straightedge, certain polygons have distinct constructions that are easily achievable. In this case, a regular pentagon is constructed by using a compass to divide the circumference of the circle into five equal parts.
To construct a regular pentagon inscribed in a circle, Ethan would start by drawing the circle using his compass. Next, he would place the compass on the circle's circumference and scribe an arc, marking one-fifth of the circumference. Then, he would move the compass to the intersection of the arc and the circle and repeat the process. The intersections of these arcs would form the vertices of the regular pentagon.
This construction is unique to the regular pentagon and doesn't apply as directly to other polygons. The equilateral triangle and the square have their specific constructions, but these do not involve dividing the circle into five equal parts. The isosceles triangle doesn't have a unique construction method for inscribing in a circle.
In summary, the process of dividing the circle into five equal parts using a compass and straightedge strongly suggests that Ethan is constructing a regular pentagon, making option (c) "A regular pentagon" the correct answer.