Incenter and Circumcenter

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 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 centroid of a triangle?

Back

The centroid is the point where the medians of a triangle intersect. It is the center of mass of the triangle.

Front

What is the orthocenter of a triangle?

Back

The orthocenter is the point where the altitudes of a triangle intersect.

Front

What is a median in a triangle?

Back

A median is a line segment that connects a vertex of the triangle to the midpoint of the opposite side.

Front

What is an altitude in a triangle?

Back

An altitude is a perpendicular segment from a vertex to the line containing the opposite side.

Front

What is an angle bisector in a triangle?

Back

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

Front

What is the special property of the circumcenter?

Back

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

Front

What is the special property of the incenter?

Back

The incenter is equally distant 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; their intersection is the circumcenter.