ADGEOM 2040

Dear friends,

Consider the following generalizations of the Simson and Steiner lines:

Let P be a point not on the circumcircle of ABC.  Let A'B'C' be the pedal triangle of P and A"B"C" the reflection triangle of P.  Define the quasi-Simson line of P as the orthic axis of A'B'C', and define the quasi-Steiner line of P as the orthic axis of A"B"C".  As P approaches a point Q on the circumcircle, the quasi-Simson/Steiner lines of P approach the Simson/Steiner lines of Q.

Any interesting results using these lines?

Best regards,
Randy Hutson