Question

James 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?
Triangle DEF is shown with two sets of intersecting arc markings on either side of side EF. A line segment is drawn through each set of intersecting arc markings and through side EF. Another segment is drawn through side DE and two more sets of intersecting arc markings.

Connect the arc markings to angle E to find another bisector
Use the compass to find the perpendicular bisector for side DF
Connect three arc markings to determine the vertices form the triangle
Use the circumcenter to determine the center of the circle

Answer 1

The correct answer is:

Use the circumcenter to determine the center of the circle .

Explanation:

The steps James has completed have constructed the perpendicular bisectors of two sides of the triangle, DE and EF. The point where the perpendicular bisectors of the sides of a triangle meet is the circumcenter of the triangle. This is also the center of the circumcircle, or circumscribed circle.

We need to extend these bisectors so that they intersect. We then set our compass on this point and set the width from this center to any vertex of the triangle. This will be the radius of the triangle; we draw the circle and are finished.