Centers of Triangles

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 centroid of a triangle?

Back

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

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 incenter of a triangle?

Back

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

Front

How do you find the length of BG if G is the centroid and BE = 18?

Back

BG = 12, since the centroid divides each median in a 2:1 ratio.

Front

What segments intersect at the circumcenter?

Back

The circumcenter is the intersection of the perpendicular bisectors of the sides of the triangle.

Front

What segments intersect at the incenter?

Back

The incenter is the intersection of the angle bisectors of the triangle.

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 twice the length of the shorter segment.

Front

What is the significance of the orthocenter in a triangle?

Back

The orthocenter can be inside, outside, or on the triangle, depending on the type of triangle (acute, obtuse, or right).

Front

What is the circumradius of a triangle?

Back

The circumradius is the radius of the circumcircle, which passes through all three vertices of the triangle.