Question

Which of the following is a step in constructing a circle circumscribed about a triangle?

Use a compass to locate the intersection of the midpoint of each side.
Use the perpendicular bisectors to find the center of the circle.
Use a compass to locate the intersection of the altitude of each side.
Use the angle bisectors to find the center of the circle.

Answer 1

• Use the perpendicular bisectors to find the center of the circle.

Step-by-step explanation:

A circle circumscribed about a triangle passes through the three vertices of the triangle.

The distance from each vertex to the center of the circle is the radius of the circle: each vertex of the triangle is at the same distance from the center of the circle.

All the points on the perpendicular bisector of a side of the triangle are at the same distance from the two vertices that define that side.

Thus, where the three perpedicular bisectors intersect each other is a point (the only one) at the same distance from the three vertices of the triangle, i.e. the center of the circle.

Hence, once the center of the circle is found, you can use a compass to draw the circle that passes through the three vertices of the triangle to construct the circle circumscribed about the triangle.