Ta có:

$\widehat{B}+\widehat{C}={{90}^{0}}$

$\widehat{CAH}+\widehat{C}={{90}^{0}}$

$\widehat{BAH}+\widehat{B}={{90}^{0}}$

$\Rightarrow \widehat{BAH}=\widehat{ACH}$

$\Rightarrow \frac{1}{2}\widehat{BAH}=\frac{1}{2}\widehat{ACH}\Rightarrow \widehat{BAI}=\widehat{IAH}=\widehat{ACI}=\widehat{ICH}$

Ta có:

$\widehat{AIC}={{180}^{0}}-\left( \widehat{CAI}+\widehat{ACI} \right)$

        $=$ ${{180}^{0}}-\left( \widehat{CAH}+\widehat{HAI}+\widehat{ACI} \right)$

         $=$ ${{180}^{0}}-\left( \widehat{CAH}+\widehat{ICH}+\widehat{ACI} \right)$

          = ${{180}^{0}}-{{90}^{0}}={{90}^{0}}$