by Brad Simmons
Finding the Center of a Circle
Use geometer's sketchpad to find the center of a circle.
1. Begin with a circle and locate three points A, B, and C on the circle.
2. Construct segment AB. Construct a segment through point B and perpendicular to segment AB. Label the perpendicular segment BD.
3. Construct segment AD. Since segment BD is perpendicular to segment AB, then the measure of angle ABD = 90 and the arc it intercepts has a measure of 180. Therefore, segment AD is a diameter.
4. Construct segment BC. Construct a segment through point B and perpendicular to segment BC. Label the perpendicular segment BF.
5. Construct segment CF. Since the measure of angle FBC = 90, segment CF is also a diameter.
6. The point that all diameters have in common is the center of the circle. Thus, the intersection of segment AD and segment CF is the center of the circle. Construct the intersection and label it point P.
Please click here for a geometer's sketchpad sketch for the figure shown above.