# Implicit Locus demo

## Example

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

## Credits

- 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)

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