Centers of Triangles

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 segments intersect at the circumcenter?

Back

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

Front

What is the orthocenter of a triangle?

Back

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

Front

What segments intersect at the orthocenter?

Back

The orthocenter is the intersection of the altitudes 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 also known as the center of mass or balance point of the triangle.

Front

What segments intersect at the centroid?

Back

The centroid is the intersection of the medians 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 segments intersect at the incenter?

Back

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

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 of the triangle and K is the area of the triangle.

Front

What is the relationship between the circumcenter and the circumradius?

Back

The circumcenter is the center of the circumcircle, which is the circle that passes through all three vertices of the triangle. The circumradius is the radius of this circumcircle.