MathTime

de **mircea.lascu** » Sâm Mar 31, 2012 6:50 pm

Fie ABCDEF un hexagon inscris intr-un cerc. Notam cu $\{M\}=AC\cap BD,$ $\{N\}=BE\cap CF$ si $\{P\}AE\cap DF$ . Aratati ca punctele M,N,P

sunt coliniare.

sursa: Vasile Pop, Cluj-Napoca

de **Virgil Nicula** » Dum Iun 03, 2012 6:13 am

PP. Fie ABCDEF un hexagon inscris intr-un cerc. Notam cu $M\in AC\cap BD$ , $N\in BE\cap CF$ si $P\in AE\cap DF$ . Aratati ca $P\in MN$ .

Proof. Apply the Pascal's theorem to the cyclical hexagon $ACFDBE\ :\ \begin{array}{c}\nearrow\\\\ \rightarrow\\\\ \searrow\end{array}\begin{array}{c} M\in AC\cap DB\\\\ N\in CF\cap BE\\\\ P\in FD\cap EA\end{array}\begin{array}{c}\searrow\\\\ \rightarrow\\\\ \nearrow\end{array}\ \implies\ P\in MN$ .

MathTime

28.03.2012 - geometrie [cls IX-XI]

28.03.2012 - geometrie [cls IX-XI]

Re: 28.03.2012 - geometrie [cls IX-XI]

Cine este conectat