Hướng chứng minh $BI // CK$: chứng minh $\widehat{IBC}+\widehat{KCB}=180^o$, suy ra song song (hai góc trong cùng phía bù nhau)
$\widehat{C_1}+\widehat{C_2}+\widehat{B_1}+\widehat{B_2}$
$=2\widehat{C_1}+2\widehat{B_2}$
$=2(\widehat{C_1}+\widehat{B_2})$ (*)
Mà trong $\Delta ABC$ có $\widehat{ABC}+\widehat{ACB}=\widehat{B_2}+\widehat{C_1}=90^o$
(vì $\widehat{BAC}=90^o$)
$\Rightarrow (*)=2.90^o=180^o$