Constructing a Circumscribed Circle on a Triangle Using Perpendicular Bisectors

This lesson teaches how to construct a circumscribed circle around a triangle using its perpendicular bisectors. It explains the concept of perpendicular bisectors, their role in determining the circumcenter, and how the circumcenter's location can vary depending on the type of triangle. The lesson provides a detailed, step-by-step guide to constructing the circumscribed circle, emphasizing the intersection of perpendicular bisectors as the circle's center.

What is a perpendicular bisector?

• A line that divides a segment into two equal parts at an angle

• A line that divides a segment into two equal parts at a right angle

• A line that divides a segment into two unequal parts

• A line that is parallel to a segment

Where is the circumcenter located in an isosceles right triangle?

• At the midpoint of the hypotenuse

• On the side of the triangle

• Outside the triangle

• Inside the triangle

What is a key property of a circumscribed circle?

• Its center is where the perpendicular bisectors of the polygon intersect

• It only touches one vertex of the polygon

• It is always smaller than the polygon

• Its center is the midpoint of one side of the polygon

What is the first step in constructing a circumscribed circle around a triangle?

• Draw a line parallel to one side of the triangle

• Find the midpoint of one side of the triangle

• Connect all the vertices of the triangle

• Draw an arc using one of the vertices of the triangle

How do you determine the radius of the circumscribed circle?

• By measuring the distance between the center and the midpoint of one side

• By measuring the distance between two vertices of the triangle

• By measuring the distance between the center and one vertex of the triangle

• By measuring the distance between the center and one side of the triangle