Incenter and Circumcenter

Front

What is the definition of the incenter of a triangle?

Back

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

Front

How can you find the incenter of a triangle?

Back

To find the incenter of a triangle, construct the angle bisectors of each of the triangle's angles. The point where all three angle bisectors intersect is the incenter.

Front

How can you find the circumcenter of a triangle?

Back

To find the circumcenter of a triangle, construct the perpendicular bisectors of each side of the triangle. The point where all three perpendicular bisectors intersect is the circumcenter.

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 is the relationship between the circumcenter and the vertices of a triangle?

Back

The circumcenter is equidistant from all three vertices of the triangle.

Front

What segments intersect at the incenter of a triangle?

Back

The angle bisectors of the triangle intersect at the incenter.

Front

What segments intersect at the circumcenter of a triangle?

Back

The perpendicular bisectors of the sides of the triangle intersect at the circumcenter.

Front

In which type of triangle is the circumcenter located inside the triangle?

Back

In an acute triangle, the circumcenter is located inside the triangle.

Front

In which type of triangle is the circumcenter located outside the triangle?

Back

In an obtuse triangle, the circumcenter is located outside the triangle.