Bellwork, Circumcenter and Incenter

Front

Define: CIRCUMCENTER OF A TRIANGLE

Back

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

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

Define: INCENTER OF A TRIANGLE

Back

The intersection point of the three angle bisectors of a triangle.

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.

Front

What is the point of concurrency of the angle bisectors called?

Back

Incenter.

Front

What is the point of concurrency of the perpendicular bisectors called?

Back

Circumcenter.

Front

If point Z is the circumcenter of ΔRST, what does that imply about distances from Z to the vertices R, S, and T?

Back

The distances from Z to R, S, and T are all equal.

Front

What is the significance of the circumcenter in triangle construction?

Back

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

Front

How can you find the circumcenter of a triangle?

Back

By constructing the perpendicular bisectors of at least two sides of the triangle.

Front

What is the significance of the incenter in triangle construction?

Back

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