Constructing Circumcircles & Incircles

Explanation

• A circumcircle passes through all vertices of a polygon.

• An incircle touches all sides of a polygon.

Key constructions:

• Circumcenter: intersection of perpendicular bisectors

• Incenter: intersection of angle bisectors

Triangles always have both a circumcircle and an incircle.

Quiz (5 Questions)

1. What is a circumcircle?

2. What is an incircle?

3. Where is the circumcenter located?

4. Where is the incenter located?

5. Which construction uses angle bisectors?

Answer Key

1. Circle through all vertices

2. Circle tangent to all sides

3. Intersection of perpendicular bisectors

4. Intersection of angle bisectors

5. Incircle