Variations on implicit loci in a triangle

Zoltán Kovács, Jul 13, 2016

GeoGebra's [b]LocusEquation[/b] command provides an easy way to get implicit locus of a condition and a mover point. This collection of applets shows basic applications of this command: all of them can be demonstrated in a classrom in the secondary school.


  • 1. Thales' theorem
  • 2. Converse of the Pythagorean theorem
  • 3. Combining Thales and Pythagoras
  • 4. Bisector (isosceles triangle)
  • 5. Appollonius' circle
  • 6. Triangle inequality
  • 7. An ellipse
  • 8. A hyperbola
  • 9. A lemniscate
  • 10. Bisector via angles (isosceles triangle)
  • 11. Funny curves

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Thales' theorem

[code]LocusEquation[a⊥b,C][/code] asks GeoGebra where to put point [i]C[/i] to ensure that the triangle is right at [i]C[/i]. Thales' theorem states that if (and only if) [i]C[/i] is a point of the circumcircle of the diameter [i]AB[/i], then the triangle is right.
– Zoltán Kovács

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