Implicit Locus demo


Question: Given a triangle ABC, AB fixed. What is the locus of points C for which ABC is a right triangle? Answer: Construct a circle whose diameter is AB and let C be any circumpoint. This question can be solved by GeoGebra from now on by using the command LocusEquation[a⟂b,C]. Here a and b are the sides of the triangle, opposite to A and B.

More simple examples

The Simson-Wallace theorem and the LocusEquation command

Numerical check of the Simson-Wallace theorem

Some details

  • Dynamic command: free points are draggable, implicit curve will be recomputed
  • In simple cases it is very fast
  • In some cases it may be unstable numerically (and may crash GeoGebra)
  • Has robust formula support (polynomial expressions)
  • Funny curves can be plotted
  • The implementation is a combination of theorem proving and implicit curves
  • Works internally with Giac (no external CAS is required)
  • Web version yet untested
  • Use --experimental to try it
  • More details in GGB-541


  • Francisco Botana (main idea)
  • Miguel A. Abánades (prototype programming in Sage/GeoGebra)
  • Tomás Recio (math background clarification)
  • Csilla Sólyom-Gecse (formula programming)
  • Zbyněk Konečný (ideas, bug fixes)
  • Zoltán Kovács (implementation, coordination)