Incenter and Circumcenter

Front

What is the definition of the incenter of a triangle?

Back

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

Front

What is the definition of the circumcenter of a triangle?

Back

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

Front

What special segments intersect at the incenter?

Back

The angle bisectors of the triangle.

Front

What special segments intersect at the circumcenter?

Back

The perpendicular bisectors of the sides of the triangle.

Front

What is a key property of the circumcenter?

Back

The circumcenter is equally distant from all three vertices of the triangle.

Front

How can you find the incenter of a triangle?

Back

By constructing the angle bisectors of the triangle and finding their intersection point.

Front

How can you find the circumcenter of a triangle?

Back

By constructing the perpendicular bisectors of the sides of the triangle and finding their intersection point.

Front

What is the relationship between the incenter and the incircle?

Back

The incenter is the center of the incircle, which is the circle inscribed within the triangle.

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 centroid of a triangle?

Back

The centroid is the point where the three medians of a triangle intersect, and it is the center of mass of the triangle.