: Relationship among some elements of triangles

The triangle DEF is inscribed in an acute-angled triangle ABC. One can drag each of the vertices of the triangles. For each size of these chosen triangles, the screen shows both the perimeter P of the triangle DEF and the ratio 2S/R, where S and R are the area and the circumradius of the triangle ABC. It’s possible to discover that P>=2S/R and that equality is obtained only when the straight lines AD, BE and FC are altitudes in the triangle ABC (i.e. when DEF is the orthic triangle).

 

gilad

 
Type de ressources
Activité
Balises
realationship  trianagles  triangles 
Tranche d'âges
13 – 19+
Langue
English
 
 
Version GeoGebra
5.0
Vues
863
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