Difference between revisions of "Trilinear Command"
From GeoGebra Manual
m |
m (Text replace - ";(.*)\[(.*)\]" to ";$1($2)") |
||
| (One intermediate revision by one other user not shown) | |||
| Line 1: | Line 1: | ||
<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|geometry}} | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|geometry}} | ||
| − | ;Trilinear | + | ;Trilinear( <Point>, <Point>, <Point>, <Number>, <Number>, <Number> ) |
| − | :creates point whose [[w:Trilinear coordinates|trilinear coordinates]] with respect to triangle with given points | + | :creates a point whose [[w:Trilinear coordinates|trilinear coordinates]] are the given numbers with respect to triangle with given points. |
| − | ==Some examples | + | ==Some examples== |
<center> | <center> | ||
{| class="wikitable" style="text-align:center;" | {| class="wikitable" style="text-align:center;" | ||
| Line 19: | Line 19: | ||
|| 0 || 0 || 1 | || 0 || 0 || 1 | ||
|- | |- | ||
| − | ! | + | ! Circumcenter |
|| cos(<math>\hat{A}</math>) || cos(<math>\hat{B}</math>) || cos(<math>\hat{C}</math>) | || cos(<math>\hat{A}</math>) || cos(<math>\hat{B}</math>) || cos(<math>\hat{C}</math>) | ||
|- | |- | ||
| Line 25: | Line 25: | ||
|| 1 || 1 || 1 | || 1 || 1 || 1 | ||
|- | |- | ||
| − | !Center of excircle | + | !Center of excircle tangent to [BC] |
||-1||1||1 | ||-1||1||1 | ||
|- | |- | ||
| − | !Center of excircle | + | !Center of excircle tangent to [AC] |
||1||-1||1 | ||1||-1||1 | ||
|- | |- | ||
| − | !Center of excircle | + | !Center of excircle tangent to [AB] |
||1||1||-1 | ||1||1||-1 | ||
|- | |- | ||
Latest revision as of 17:16, 7 October 2017
- 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}) |
