a,
$\widehat{B}=2\widehat{C}$
Đặt $\widehat{B}=2x \Rightarrow \widehat{C}=x$
$\widehat{B}+\widehat{C}=180^o-\widehat{C}=180-60=120^o$
$\Rightarrow x+2x=120$
$\Leftrightarrow x=40$
Vậy $\widehat{B}=80^o,\widehat{C}=40^o$
$\widehat{C}<\widehat{A}<\widehat{B}$
$\Rightarrow$ AB < BC < AC
b,
$\Delta$ AHI và $\Delta$ AKI có:
$\widehat{AHI}=\widehat{AKI}=90^o$
AI chung
$\widehat{HAI}=\widehat{KAI}$
$\Rightarrow \Delta$ AHI = $\Delta$ AKI (ch-gn)
$\Rightarrow$ HI= HK
c, (Chưa ra)