To construct a circle from three given points using a compass and straightedge, follow these steps:
- Draw two line segments connecting the three given points. Suppose the points are A, B, and C. Draw segment AB and segment BC.
- Bisect segment AB:
- Place the compass at A and set the radius to be more than half of AB.
- Draw arcs above and below AB.
- Without changing the compass width, repeat from B, creating two intersection points.
- Draw a straight line through these intersections—this is the perpendicular bisector of AB.
- Bisect segment BC using the same method as above to find its perpendicular bisector.
- Find the circumcenter:
- The two perpendicular bisectors will intersect at a point; this is the circumcenter of the triangle formed by A, B, and C.
- This point is equidistant from all three given points.
- Draw the circumcircle:
- Set the compass on the circumcenter and adjust its radius to reach any of the three points.
- Draw the circle, which will pass through all three given points.
Animation:
