Triangle Centers

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 the vertices of the triangle.

Front

What are the properties of the circumcenter in relation to a triangle?

Back

The circumcenter is equidistant from all three vertices of the triangle and can be located inside, on, or outside the triangle depending on the type of triangle (acute, right, or obtuse).

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 known as the center of mass or barycenter.

Front

How is the centroid related to the vertices 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.

Front

What is the orthocenter of a triangle?

Back

The orthocenter is the point where the three altitudes of a triangle intersect. Its position varies depending on the type of 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 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.

Front

What is a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a 90-degree angle.

Front

What is the significance of the circumcenter in triangle construction?

Back

The circumcenter can be used to construct the circumcircle of a triangle, which is useful in various geometric applications.

Front

What is the relationship between the orthocenter and the circumcenter in an acute triangle?

Back

In an acute triangle, the orthocenter lies inside the triangle, while the circumcenter also lies inside the triangle.