Incenter and Circumcenter

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 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 Incenter?

Back

The Incenter is the intersection of the angle bisectors of a triangle.

Front

What is the relationship between the Incenter and the triangle's sides?

Back

The Incenter is equidistant from all three sides of the triangle, meaning it is the center of the circle inscribed within the triangle.

Front

What is the relationship between the Circumcenter and the triangle's vertices?

Back

The Circumcenter is equidistant from all three vertices of the triangle, meaning it is the center of the circumcircle that passes through all three vertices.

Front

How do you find the Incenter of a triangle?

Back

To find the Incenter, construct the angle bisectors of each angle in the triangle and locate their intersection point.

Front

How do you find the Circumcenter of a triangle?

Back

To find the Circumcenter, construct the perpendicular bisectors of each side of the triangle and locate their intersection point.

Front

What is an angle bisector?

Back

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

Front

What is a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a 90-degree angle.

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 the center of mass of the triangle.