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Discovering the Simson-Wallace theorem

  1. Given the triangle ABC.
  2. Construct the lines of the sides.
  3. Let D be an arbitrary point.
In Steps 4-9 we create the perpendicular projection of D to the lines constructed in Step 2. Is it possible to choose D in order to be the projection points (feet points E, F and G) aligned? In Step 10 GeoGebra solves this question by computing LocusEquation[AreCollinear[E,F,G],D].