Question

michael is constructing a circle circumscribed about a triangle. he has partially completed the construction. what should be his next step in the construction?

Explanation:

Step1: Recall circumscribed circle construction

To construct a circle circumscribed about a triangle (circum - circle), we need to find the circum - center. The circum - center is the intersection of the perpendicular bisectors of the sides of the triangle.

Step2: Analyze the given construction

The marks (the crosses) in the figure likely represent the arcs drawn for constructing the perpendicular bisectors of the sides of \(\triangle DEF\). Since we need two perpendicular bisectors to find their intersection (the circum - center), and if we assume that one perpendicular bisector is partially constructed (from the given arcs), the next step is to construct the perpendicular bisector of another side.

Answer:

Construct the perpendicular bisector of another side of the triangle.