Incenter and Circumcenter

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

Which special segments intersect at the incenter?

Back

Angle Bisectors.

Front

Which special segments intersect at the circumcenter?

Back

Perpendicular Bisectors.

Front

What is the centroid of a triangle?

Back

The centroid is the point where the medians of a triangle intersect. It is the center of mass 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

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

How do you find the inradius of a triangle?

Back

The inradius (r) 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 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 the relationship between the incenter and the incircle?

Back

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