Tetraedru echifacial
Moderators: Bogdan Posa, Laurian Filip
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Marius Mainea
- Gauss
- Posts: 1077
- Joined: Mon May 26, 2008 2:12 pm
- Location: Gaesti (Dambovita)
Tetraedru echifacial
Sa se arate ca daca cercurile circumscrise fetelor unui tetraedru au raze egale, atunci muchiile opuse ale tetraedrului sunt congruente doua cate doua.
In cercuri egale la coarde egale corespund unghiuri egale .
\( \Rightarrow [AD] \) ; \( \angle ACD=\angle ABD \)
\( [AB] \) ; \( \angle ACB=\angle ADB \)
\( [BD] \) ; \( \angle BAD=\angle BCD \)
Desfasuram tetraedrul \( \Rightarrow \angle A_1CB+\angle BCD+\angle DCA_3=\angle A_2DB+\angle BA_2D+\angle A_2BD=180 \) \( \Rightarrow \) \( A_1 , C , A_3 \) - coliniare ; \( \Delta BCD \) - triunghi median \( \Rightarrow A_2B=CD \) .
\( \Rightarrow [AD] \) ; \( \angle ACD=\angle ABD \)
\( [AB] \) ; \( \angle ACB=\angle ADB \)
\( [BD] \) ; \( \angle BAD=\angle BCD \)
Desfasuram tetraedrul \( \Rightarrow \angle A_1CB+\angle BCD+\angle DCA_3=\angle A_2DB+\angle BA_2D+\angle A_2BD=180 \) \( \Rightarrow \) \( A_1 , C , A_3 \) - coliniare ; \( \Delta BCD \) - triunghi median \( \Rightarrow A_2B=CD \) .
. A snake that slithers on the ground can only dream of flying through the air.