---
tag: BFD7T0YY42
kind: concept
name: Radical axis
msc: [51M04]
sources:
  - url: https://en.wikipedia.org/wiki/Radical_axis
same_as:
  wikidata: Q2106473
  wikipedia: Radical axis
---

## Summary

The radical axis of two non-concentric [[circles|060W5CBZP6]] is the set of points that have the same [[power|02E9VT1RVQ]] with respect to both circles.
It is a straight line perpendicular to the line through the two centres.
When the circles meet in two points, it is the line through those points.
Radical axes give short proofs of many concurrency and collinearity results.

## Explanations

### L1 human

From a point outside a circle, draw a tangent segment to the circle.
The radical axis of two circles is where these tangent segments to the two circles have equal length.
If two circles cross, the radical axis is the line through their two crossing points.
For example, the unit circles centred at $(0, 0)$ and $(2, 0)$ touch at $(1, 0)$, and their radical axis is the vertical line $x = 1$.