### Morley's Theorem

What if applet does not run? |

The locus of the incenters of the cardioids that touch 3 lines are in *general position* is a union of three sets of three parallel lines forming angles of 60° (and, naturally, 120°.) These are the *axes* of the 3-line. Naturally, the axes form equilateral triangles - 27 of them. An important observation is that the vertices of these triangles - the points where two axes meet - have the property that the corresponding cardioid touches one of the given lines (of the 3-line) twice.

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