Difference between revisions of "Trilinear Command"
From GeoGebra Manual
(Created page with "<noinclude>{{Manual Page|version=4.2}}</noinclude> {{command|geometry}} ;Trilinear[<Point A>,<Point B>,<Point C>,<Number a>, <Number b>, <Number c>] :creates point whose [[w:Tr...") |
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| − | <noinclude>{{Manual Page|version= | + | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|geometry}} |
| − | {{command|geometry}} | + | ;Trilinear( <Point>, <Point>, <Point>, <Number>, <Number>, <Number> ) |
| − | ;Trilinear | + | :creates a point whose [[w:Trilinear coordinates|trilinear coordinates]] are the given numbers with respect to triangle with given points. |
| − | :creates point whose [[w:Trilinear coordinates|trilinear coordinates]] with respect to | + | |
| + | |||
| + | ==Some examples== | ||
| + | <center> | ||
| + | {| class="wikitable" style="text-align:center;" | ||
| + | |- | ||
| + | ! Point !! <Number> !! <Number> !! <Number> | ||
| + | |- | ||
| + | ! A | ||
| + | || 1 || 0 || 0 | ||
| + | |- | ||
| + | ! B | ||
| + | || 0 || 1 || 0 | ||
| + | |- | ||
| + | ! C | ||
| + | || 0 || 0 || 1 | ||
| + | |- | ||
| + | ! Circumcenter | ||
| + | || cos(<math>\hat{A}</math>) || cos(<math>\hat{B}</math>) || cos(<math>\hat{C}</math>) | ||
| + | |- | ||
| + | ! 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 | ||
| + | || <math>\frac{1}{a}</math> || <math>\frac{1}{b}</math> || <math>\frac{1}{c}</math> | ||
| + | |- | ||
| + | ! Orthocenter | ||
| + | || cos(<math>\hat{B}</math>) cos(<math>\hat{C}</math>) || cos(<math>\hat{A}</math>) cos(<math>\hat{C}</math>) || cos(<math>\hat{A}</math>)cos(<math>\hat{B}</math>) | ||
| + | |} | ||
| + | </center> | ||
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}) |
