Inscribe and Circumscribe Circles
in and around Triangles
To inscribe a circle within a triangle:
- Bisect all three angles
- Draw a circle with
- Center where all three angle bisectors intersect, and
- Radius equal to the closest distance from the center to all three sides.
To circumscribe a circle around a triangle:
- Draw the perpendicular bisectors of all three sides
- Draw a circle with
- Center where all three perpendicular bisectors intersect, and
- Radius equal to the furthest distance from the center to all three vertices.