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 varies depending on the type of triangle (acute, right, or obtuse).

Front

If point P is the circumcenter, which segment is equal to PB?

Back

PC

Front

What type of point of concurrency is the incenter?

Back

The incenter is the point of concurrency of the angle bisectors of a triangle.

Front

If CF, BE, and AD are the medians of the triangle and BF = 10, what is AF?

Back

10

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

How do you find the inradius of a triangle?

Back

The inradius can be found using the formula r = A/s, where A is the area of the triangle and s is the semi-perimeter.

Front

What is the significance of the centroid in a triangle?

Back

The centroid is the balance point of the triangle and divides each median into a 2:1 ratio.