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 can be inside, on, or outside the triangle depending on the type of triangle.

Front

What are medians in a triangle?

Back

Medians are line segments that connect a vertex of the triangle to the midpoint of the opposite side.

Front

What is the relationship between the centroid and the medians?

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 side.

Front

Which points of concurrency are always inside a triangle?

Back

The incenter and centroid are always located inside the triangle.

Front

What is the significance of the circumcenter in relation to the triangle's 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 significance of the incenter in relation to the triangle's incircle?

Back

The incenter is the center of the incircle, which is the circle that is tangent to all three sides of the triangle.