Circumcenter and Incenter

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 is the special property of the incenter?

Back

The distance from the incenter to each side of the triangle is the same.

Front

What is the special property of the circumcenter?

Back

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

Front

Which segments intersect at the incenter?

Back

Angle bisectors.

Front

Which segments intersect at the circumcenter?

Back

Perpendicular bisectors.

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 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.