Circumcenter, Incenter, centroid, orthocenter

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.

Tags

CCSS.HSG.CO.C.10

Front

Define 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.

Tags

CCSS.HSG.C.A.3

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.

Tags

CCSS.HSG.C.A.3

Front

What is the orthocenter of a triangle?

Back

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

Tags

CCSS.HSG.CO.C.10

Front

If G is the centroid of triangle ABC and AG = 16, what is the length of GD?

Back

8 (The centroid divides each median into a ratio of 2:1.)

Tags

CCSS.HSG.CO.C.10

Front

What type of point of concurrency is the circumcenter?

Back

The circumcenter is the point of concurrency of the perpendicular bisectors of a triangle.

Tags

CCSS.HSG.C.A.3

Front

What type of point of concurrency is the incenter?

Back

The incenter is the point of concurrency of the angle bisectors of a triangle.

Tags

CCSS.HSG.C.A.3

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.

Tags

CCSS.HSG.C.A.3

Front

How do you find the circumcenter of a triangle given its vertices?

Back

To find the circumcenter, calculate the intersection of the perpendicular bisectors of at least two sides of the triangle.

Tags

CCSS.HSG.C.A.3

Front

What is the significance of the centroid in a triangle?

Back

The centroid is the balance point of the triangle and divides each median into a 2:1 ratio.

Tags

CCSS.HSG.CO.C.10