Circumscribing a Circle About a Triangle & Inscribing a Circle Inside a Triangle.

Given triangle ABC. We want to circumscribed circle D about triangle ABC.

First we will construct perpendicular bisectors of any two sides of triangle ABC, intersecting at D, which is the circumcenter of the given triangle.

With center D, draw a circle D with radius DA. Therefore circle D, which passes through points A, B, and C, will circumscribe the triangle ABC.

Inscribing a Circle inside a Triangle

1. Construct the angle bisectors of the angles of a triangle.

2. The point of intersection of the angle bisectors is the incenter.

3. From the incenter construct segments that are perpendicular to the sides of the triangle. This segment is called the apothem.

4. Use the line from the incenter and perpendicular to the side of the triangles as the radius for the circle to be drawn inside the triangle.