Properties of Triangle Centers

Front

What is an angle bisector?

Back

An angle bisector is a line or segment that divides an angle into two equal parts.

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.

Front

What is the incenter of a triangle?

Back

The incenter is the point where the angle bisectors of a triangle intersect, and it is the center of the triangle's incircle.

Front

What is a median in a triangle?

Back

A median is a line segment that connects a vertex of a triangle 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 centroid of a triangle?

Back

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

Front

What is the orthocenter of a triangle?

Back

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

Front

How do you find the circumradius of a triangle?

Back

The circumradius (R) can be found using the formula R = (abc)/(4K), where a, b, and c are the lengths of the sides and K is the area of the triangle.

Front

What is the relationship between the incenter and the incircle?

Back

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

Front

What is the significance of the centroid in a triangle?

Back

The centroid divides each median into a ratio of 2:1, with the longer segment being closer to the vertex.