Concursul Matefbc editia a 4-a problema 4

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Andi Brojbeanu
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Concursul Matefbc editia a 4-a problema 4

Post by Andi Brojbeanu »

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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