Răspuns :

Semaka2id

Răspuns:

<H este inscris in semicerc=><H=90°=>

Triunghiul GHE=dreptunghic

HG=AG

Dar AG=raza=>GE=2AG=2HG

Deci ipotenuuza GE=2HG=><BEG=30°

Dar<BEG≡<IEJ=30°

<IJE este  complementarul <IEJ=>

<IJE=90-30=60°

Explicație pas cu pas:

Targoviste44id

[tex]\it Compar\breve am\ \Delta GHE\ cu\ \Delta JIE\\ \\ \\ \left.\begin{aligned} \it \widehat{GHE}=\widehat{JIE}=90^o\\\ (\ cuprind\ diametru\ de\ cerc )\\ \\ \it \widehat{HEG}=\widehat{IEJ}\ (opuse\ la\ v\hat arf) \end{aligned}\right\} \stackrel{UU}{\Longrightarrow} \Delta GHE\ \sim\ \Delta JIE \Rightarrow \widehat{IJE}=\widehat{EGH}\ \ \ \ \ (1)[/tex]

[tex]HG=AG,\ \ AG=AH\ (raze) \Rightarrow \Delta AGH-echilateral \Rightarrow \widehat{EGH}= \it60^o \ \ \ \ (2)\\ \\ (1),\ (2) \Rightarrow \widehat{IJE}=60^o[/tex]

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