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PonceletPoint

The tan-colored rotating triangle *a(t)b(t)c(t)* has the same orientation as triangle *ABC*. Lines *B*-to-*b(t)* and *C*-to-*c(t)* meet in a point *u*, and points *v* and *w* are defined cyclically. The orbits of *u*, *v*, and *w* concur in a point. Thus, as the triangle rotates, there is only one position in which the lines *A*-to-*a(t)*, *B*-to-*b(t)*, and *C*-to-*c(t)* concur.
For more, see *GEOMETRY IN ACTION*, Chapter 7.