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Concursul Matefbc editia a 4-a problema 4

 
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Andi Brojbeanu
Newton


Joined: 22 Mar 2009
Posts: 383
Location: Targoviste (Dambovita)

PostPosted: Sun Dec 06, 2009 9:57 pm    Post subject: Concursul Matefbc editia a 4-a problema 4 Reply with quote

Triunghiul dreptunghic ABC(m(\widehat{B})=90\textdegree) contine "zig-zagul" AM_1=M_1N_1=N_1M_2=M_2N_2=N_2B=AB, unde M_1, M_2 \in (AB), N_1, N_2\in (AC), M_1\in (AM_2) si N_1\in (AN_2).
a) Aflati masura unghiului A;
b) Aratati ca printre triunghiurile astfel formate exista un triunghi echilateral. Care este acesta?
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