Trilinear Command
From GeoGebra Manual
- Trilinear( <Point>, <Point>, <Point>, <Number>, <Number>, <Number> )
- creates a point whose trilinear coordinates are the given numbers with respect to triangle with given points.
Some examples
| Point | <Number> | <Number> | <Number> |
|---|---|---|---|
| A | 1 | 0 | 0 |
| B | 0 | 1 | 0 |
| C | 0 | 0 | 1 |
| Circumcenter | cos(\hat{A}) | cos(\hat{B}) | cos(\hat{C}) |
| Center of Incircle | 1 | 1 | 1 |
| Center of excircle tangent to [BC] | -1 | 1 | 1 |
| Center of excircle tangent to [AC] | 1 | -1 | 1 |
| Center of excircle tangent to [AB] | 1 | 1 | -1 |
| Centroid | \frac{1}{a} | \frac{1}{b} | \frac{1}{c} |
| Orthocenter | cos(\hat{B}) cos(\hat{C}) | cos(\hat{A}) cos(\hat{C}) | cos(\hat{A})cos(\hat{B}) |
