Circle Touching 3 Points
How to construct a Circle touching 3 Points
using just a compass and a straightedge
images/construct.js?mode=circle3pts
Steps:
- Join up the points to form two lines
- Construct the perpendicular bisector of one line
- Construct the perpendicular bisector of the other line
- Where they cross is the center of the circle
- Place compass on the center point, adjust its length to reach any point, and draw your circle!
Note: this is the same method as Circumscribe a Circle on a Triangle
Important: The 3 points must not be on one straight line (not collinear). If they are collinear, there's no single circle that goes through all 3 points.
Why does this work?
It's like magic, but it's pure math!
Calling the points A, B and C:
- Every point on the perpendicular bisector of line AB is the exact same distance from A and B
- Every point on the perpendicular bisector of line BC is the exact same distance from B and C
- So, the point where they cross must be the exact same distance from A, B, and C!
That crossing point is the perfect center for our circle.