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 all three vertices of the triangle.

Front

What segments are drawn to find the centroid of a triangle?

Back

Medians are drawn to find the centroid of a triangle.

Front

Where is the incenter located in a triangle?

Back

The incenter is always located inside a triangle.

Front

What is the centroid of a triangle?

Back

The centroid is the point of concurrency of the three medians of a triangle.

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 equidistant from all three sides of the triangle.

Front

What is the relationship between the circumcenter and the vertices of a triangle?

Back

The circumcenter is equidistant from all three vertices of the triangle.

Front

What type of triangle center is the centroid?

Back

The centroid is a type of triangle center that represents the average position of all the points in the triangle.

Front

How can you find the circumcenter of a triangle?

Back

To find the circumcenter, construct the perpendicular bisectors of at least two sides of the triangle; their intersection point is the circumcenter.

Front

What is the significance of the incenter in triangle geometry?

Back

The incenter is significant because it is the center of the inscribed circle (incircle) of the triangle, which touches all three sides.

Front

What is the relationship between the centroid and the area of a triangle?

Back

The centroid divides each median into two segments, with the longer segment being twice the length of the shorter segment, thus affecting the area calculations.