Circumcenter / Incenter

Front

What is the Circumcenter of a triangle?

Back

The point where the perpendicular bisectors of the sides of a triangle intersect.

Tags

CCSS.HSG.C.A.3

Front

What is the Incenter of a triangle?

Back

The point where the angle bisectors of a triangle intersect, which is also the center of the circle inscribed in the triangle.

Tags

CCSS.HSG.C.A.3

Front

What is the Circumcenter Theorem?

Back

The distances from the vertices to the circumcenter are congruent.

Tags

CCSS.HSG.C.A.3

Front

How do you find the Circumcenter of a triangle?

Back

By constructing the perpendicular bisectors of at least two sides of the triangle and finding their intersection.

Tags

CCSS.HSG.C.A.3

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.

Tags

CCSS.HSG.C.A.3

Front

What is the relationship between the Incenter and the sides of a triangle?

Back

The incenter is equidistant from all three sides of the triangle.

Tags

CCSS.HSG.C.A.3

Front

What is a perpendicular bisector?

Back

A line that divides a segment into two equal parts at a right angle.

Front

What is an angle bisector?

Back

A line that divides an angle into two equal angles.

Tags

CCSS.HSG.CO.C.9

Front

What is the significance of the Circumcenter in a triangle?

Back

It is the center of the circumcircle, the circle that passes through all three vertices.

Tags

CCSS.HSG.C.A.3

Front

What is the significance of the Incenter in a triangle?

Back

It is the center of the incircle, the circle that is tangent to all three sides.

Tags

CCSS.HSG.C.A.3