Incenter and Circumcenter

Front

What is the circumcenter of a triangle?

Back

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

Front

What is the incenter of a triangle?

Back

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

Front

What segments intersect at the incenter?

Back

The incenter is the intersection of the angle bisectors of a 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 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

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 circumradius?

Back

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

Front

What is the inradius?

Back

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

Front

What is the significance of the circumcenter in triangle construction?

Back

The circumcenter can be used to construct the circumcircle of the triangle, which is useful in various geometric applications.