Circumcenter, Incenter, centroid, orthocenter

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 centroid of a triangle?

Back

The centroid is the point where the three medians of a triangle intersect. It is the center of mass and divides each median into a 2:1 ratio.

Front

What is the orthocenter of a triangle?

Back

The orthocenter is the point where the three altitudes of a triangle intersect. Its position varies depending on the type of triangle (acute, right, or obtuse).

Front

What is a median in a triangle?

Back

A median is a line segment that connects a vertex of a 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 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

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

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.

Front

How do you find the incenter of a triangle?

Back

To find the incenter, construct the angle bisectors of all three angles of the triangle. The point where they intersect is the incenter.