Triangle Centers

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, and it is equidistant from all three vertices.

Front

How do you find the circumcenter of a triangle?

Back

To find the circumcenter, draw the perpendicular bisectors of at least two sides of the triangle; their intersection point is the circumcenter.

Front

What is 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.

Front

How do you find the incenter of a triangle?

Back

To find the incenter, draw the angle bisectors of all three angles of the triangle; their intersection point is the incenter.

Front

What is an angle bisector?

Back

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

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.

Front

How do you find the centroid of a triangle?

Back

To find the centroid, draw the medians from each vertex to the midpoint of the opposite side; their intersection point is the centroid.

Front

What is the orthocenter of a triangle?

Back

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

Front

How do you find the orthocenter of a triangle?

Back

To find the orthocenter, draw the altitudes from each vertex to the opposite side; their intersection point is the orthocenter.

Front

What is the relationship between the circumcenter and the circumradius?

Back

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