sin cos khó

V

vy000

Ta có:
$\widehat{AIB}=\widehat{AHB}=90^o$

$\Rightarrow AIBH$ là tứ giác nội tiếp

$\Rightarrow \begin{cases}\widehat{CIH}=\widehat{CBA}\\\widehat{CHI}=\widehat{CAB}\end{cases}$

$\Rightarrow \Delta CHI~\Delta CAB$

$\Rightarrow \dfrac{HI}{AB}=\dfrac{CH}{CA}=\cos \widehat{C}$

$\Leftrightarrow HI=AB\cos \widehat{C}$

Tương tự:

$KI=BC\cos \widehat{A}$
$KH=AC\cos \widehat{B}$

$\Rightarrow \text{đpcm}$
 
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