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 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 vertices of the triangle.

Front

What segments intersect at the Incenter?

Back

Angle Bisectors.

Front

What segments intersect at the Circumcenter?

Back

Perpendicular Bisectors.

Front

What is a key property of the Incenter?

Back

The distance from the Incenter to each side of the triangle is the same.

Front

How do you find the Incenter of a triangle?

Back

To find the Incenter, construct the angle bisectors of each angle of 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 the relationship between the Incenter and the triangle's sides?

Back

The Incenter is the center of the circle inscribed within the triangle, touching all three sides.

Front

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

Back

The Circumcenter is the center of the circle circumscribed around the triangle, passing through all three vertices.

Front

If the Incenter is at point P, what can be said about the distances to the sides of the triangle?

Back

The distances from point P to each side of the triangle are equal.