Centers of Triangles

Front

What is the circumcenter of a triangle?

Back

The circumcenter is the point where the three perpendicular bisectors 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 of concurrency of the three medians of a triangle. It divides each median into two segments, with the longer segment being two-thirds the length of the entire median.

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 angle bisector?

Back

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

Front

What is the point of concurrency of the three medians called?

Back

The point of concurrency of the three medians is called the centroid.

Front

What is the relationship between the centroid and the medians of a triangle?

Back

The centroid divides each median into two segments, with the longer segment being two-thirds the length of the entire median.

Front

What is the circumradius of a triangle?

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 incenter of a triangle?

Back

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

Front

What is a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a line segment into two equal parts at a right angle.

Front

What is the relationship between the circumcenter and the circumradius?

Back

The circumcenter is the center of the circumcircle, and the circumradius is the distance from the circumcenter to any vertex of the triangle.