Inegalitate in tetraedrul tridreptunghic
Scris: Dum Apr 23, 2017 6:29 am
Fie $OABC-$un tetraedru tridreptunghic in $O(OA\perp OB\perp OC\perp OA)$ si $H:=pr_{(ABC)}(O).$
Notam cu $S_a,S_b,S_c-$ariile fetelor opuse varfurilor $A,B$ si respectiv $C;$ iar cu $h:=|OH|.$
Aratati ca are loc inegalitatea: $\boxed{\dfrac{1}{h^2}\ge\dfrac{S_a}{S_b^2+S_c^2}+\dfrac{S_b}{S_a^2+S_c^2}+\dfrac{S_c}{S_a^2+S_b^2}}.$ (Catalin Calistru-IASI)
Notam cu $S_a,S_b,S_c-$ariile fetelor opuse varfurilor $A,B$ si respectiv $C;$ iar cu $h:=|OH|.$
Aratati ca are loc inegalitatea: $\boxed{\dfrac{1}{h^2}\ge\dfrac{S_a}{S_b^2+S_c^2}+\dfrac{S_b}{S_a^2+S_c^2}+\dfrac{S_c}{S_a^2+S_b^2}}.$ (Catalin Calistru-IASI)