5-1 Circumcenter & Incenter

Front

What is the incenter of a triangle?

Back

The incenter of a triangle is the point where the three angle bisectors intersect. It is equidistant from all sides of the triangle.

Front

What is the circumcenter of a triangle?

Back

The circumcenter of a triangle is the point where the three perpendicular bisectors of the sides intersect. It is equidistant from all three vertices of the triangle.

Front

How do you find the circumcenter of a triangle?

Back

To find the circumcenter, construct the perpendicular bisectors of at least two sides of the triangle. The point where they intersect is the circumcenter.

Front

How do you find the incenter of a triangle?

Back

To find the incenter, construct the angle bisectors of at least two angles of the triangle. The point where they intersect is the incenter.

Front

What is the relationship between the incenter and the sides of a triangle?

Back

The incenter is equidistant from all three sides of the triangle.

Front

What theorem is used to find distances related to the circumcenter?

Back

The Perpendicular Bisector Theorem is used to find distances related to the circumcenter.

Front

What theorem is used to find distances related to the incenter?

Back

The Angle Bisector Theorem is used to find distances related to the incenter.

Front

If a triangle has vertices A, B, and C, how do you find the circumradius?

Back

The circumradius can be found using the formula R = (abc)/(4K), where a, b, and c are the lengths of the sides and K is the area of the triangle.

Front

What is the significance of the circumcenter in a triangle?

Back

The circumcenter is the center of the circumcircle, which is the circle that passes through all three vertices of the triangle.

Front

What is the significance of the incenter in a triangle?

Back

The incenter is the center of the incircle, which is the circle that is tangent to all three sides of the triangle.