Question

demonstrati ca triunghiul abc este isoscel a=2b cos c

Answer 1

[tex]\it a=2b cos C =2b\dfrac{a^2+b^2-c^2}{2ab} =\dfrac{a^2+b^2-c^2}{a} \Longrightarrow \\\;\\ \Longrightarrow \it a^2= a^2+b^2-c^2 \Longrightarrow b^2-c^2=0 \Longrightarrow (b-c)(b+c) = 0 \\\;\\ \Longrightarrow \it b-c = 0 \Longrightarrow b = c \Longrightarrow \Delta ABC - \ isoscel,\ AC=AB[/tex]