by Brad Simmons
Circle Inscribed in a Polygon
Use geometer's sketchpad to inscribe a circle in a polygon.
Construct a circle inscribed in a given triangle ABC.
1. Construct the angle bisectors of angle A and angle C. Label the intersection of the two angle bisectors point X.
2. Construct a line from X and perpendicular to segment AC. Label the intersection (of the perpendicular line and segment AC) point Y.
3. Select the two angle bisectors. Select the perpendicular line. Hide the objects. Construct segment XY.
4. Select point X and segment XY. Construct circle by center and radius.
5. Select segment XY. Hide the segment.
Circle X is inscribed in triangle ABC. Sides AB, BC, and AC are tangent to circle X.
Please click here for a geometer's sketchpad sketch of the figure shown above.