Circumcenter & Incenter

Front

What is the circumcenter of a triangle?

Back

The circumcenter is the point where the three perpendicular bisectors of a triangle intersect.

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; their intersection point is the circumcenter.

Front

What is the incenter of a triangle?

Back

The incenter is the point where the three angle bisectors of a triangle intersect.

Front

How do you find the incenter of a triangle?

Back

To find the incenter, construct the angle bisectors of all three angles of the triangle; their intersection point is the incenter.

Front

What is the relationship between the circumcenter and the circumcircle?

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 relationship between the incenter and the incircle?

Back

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

Front

What is a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a 90-degree angle.

Front

What is an angle bisector?

Back

An angle bisector is a line that divides an angle into two equal angles.

Front

What is the significance of the circumcenter in triangle geometry?

Back

The circumcenter is equidistant from all three vertices of the triangle, making it useful for constructing the circumcircle.

Front

What is the significance of the incenter in triangle geometry?

Back

The incenter is equidistant from all three sides of the triangle, making it useful for constructing the incircle.