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2014-05-29T13:17:19+03:00
\displaystyle A=\frac{(a+b)^2}{8}

\displaystyle A=\frac{ab}{2}.

\displaystyle \Rightarrow\frac{(a+b)^2}{8}=\frac{ab}{2}.

Notam t=\text{tg}(BAC).

Atunci  t=\frac{b}{a}\Rightarrow b=at

Inlocuim: \displaystyle \frac{(a+at)^2}{8}=\frac{a\cdot at}{2}

\displaystyle \frac{a^2(1+t)^2}{8}=\frac{a^2t}{2}

\displaystyle \frac{(1+t)^2}{4}=t

(1+t)^2=4t \\  \\ t^2+2t+1=4t \\  \\ t^2-2t+1=0 \\  \\ (t-1)^2=0\Rightarrow t=1.

Deci m(BAC)=45 grade

Prin urmare si m(ABC)=45.
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