Maths & numbers
Circle intersection points
Find the intersection coordinates of two circles and view their geometry.
A clear answer. Here’s how.
Uses centre separation, the radical-axis foot and perpendicular offsets. Returns zero, one tangent point, or two crossing points. Concentric unequal circles have no crossing; coincident circles are rejected as infinitely many intersections. Radii must be positive and use the coordinate unit. A relative tolerance of about 10⁻¹⁰ distinguishes tangency and coincidence; very near-degenerate geometry is approximate.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- Circle A centre X
- 0
- Circle A centre Y
- 0
- Circle A radius
- 5
- Circle B centre X
- 6
- Circle B centre Y
- 0
- Circle B radius
- 5
Example result
| Point | X | Y |
|---|---|---|
| 1 | 3 | 4 |
| 2 | 3 | -4 |
2 distinct intersection points.