Circumcenter, incenter, orthocenter, centroid

Front

What is the centroid of a triangle?

Back

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

Front

If X is the centroid of triangle ABC and BX = 8, what is BY?

Back

12

Front

Which point in a triangle is equidistant from the sides?

Back

Incenter

Front

Which point in a triangle is equidistant from the vertices?

Back

Circumcenter

Front

What is a median in a triangle?

Back

A median is a line segment joining a vertex 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 incenter of a triangle?

Back

The incenter is the point where the three angle bisectors of a triangle intersect.

Front

What is the circumcenter of a triangle?

Back

The circumcenter is the point where the three perpendicular bisectors of a triangle intersect.

Front

What is the orthocenter of a triangle?

Back

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

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 segment connecting the centroid to the vertex being twice as long as the segment connecting the centroid to the midpoint of the opposite side.