Question

aaron is constructing a circle circumscribed about a triangle. he has partially completed the construction, as shown below. what should be his next step in the construction? connect the arc markings to angle e to find another bisector.

Explanation:

Step1: Recall circum - circle construction

To construct a circle circumscribed about a triangle, we first find the circum - center. The circum - center is the point of intersection of the perpendicular bisectors of the sides of the triangle.

Step2: Analyze the given construction

The red - marked lines in the figure are the perpendicular bisectors of two sides of the triangle $\triangle DEF$. The next step is to find the point of intersection of these perpendicular bisectors.

Step3: Identify the final step

Once the point of intersection of the perpendicular bisectors (circum - center) is found, we can use it as the center of the circle and its distance to any of the vertices of the triangle as the radius to draw the circum - circle. So the next step is to find the point of intersection of the two constructed perpendicular bisectors.

Answer:

Find the point of intersection of the two constructed perpendicular bisectors.