Ai làm nhanh đúng 5 sao và 1 cảm ươn Có vẽ hình nhaaa

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$\color{darkgoldenrod}{1)}\ \text{Xét}\ \triangle AHN\ \text{và}\ \triangle ABP\ \text{có:}$

$\hspace{0.65cm}\ \widehat{A}\ \text{chung}$

$\hspace{0.65cm}\ \widehat{ANH}=\widehat{APB}\ (=90^\circ)$

$\Rightarrow\ \triangle AHN\ \backsim\ \triangle ABP\ \text{(g - g)}$

$\Rightarrow\ \dfrac{AN}{AP}=\dfrac{AH}{AB}$

$\Leftrightarrow\ AN.AB=AH.AP\ \color{red}{(1)}$

$\hspace{0.65cm}\ \text{Xét}\ \triangle AHM\ \text{và}\ \triangle ACP\ \text{có:}$

$\hspace{0.65cm}\ \widehat{A}\ \text{chung}$

$\hspace{0.65cm}\ \widehat{AMH}=\widehat{APC}\ (=90^\circ)$

$\Rightarrow\ \triangle AHM\ \backsim\ \triangle ACP\ \text{(g - g)}$

$\Rightarrow\ \dfrac{AM}{AP}=\dfrac{AH}{AC}$

$\Leftrightarrow\ AH.AP=AM.AC\ \color{red}{(2)}$ 

$\hspace{0.65cm}\ \text{Từ}\ \color{red}{(1)}\ \text{và}\ \color{red}{(2)}\ \Rightarrow\ AN.AB=AH.AP=AM.AC\ \text{(đpcm)}$

$\\$
$\color{darkgoldenrod}{2)}\ \text{Xét}\ \triangle BHN\ \text{và}\ \triangle BAM\ \text{có:}$

$\hspace{0.65cm}\ \widehat{B}\ \text{chung}$

$\hspace{0.65cm}\ \widehat{BNH}=\widehat{BMA}\ (=90^\circ)$

$\Rightarrow\ \triangle BHN\ \backsim\ \triangle BAM\ \text{(g - g)}$

$\Rightarrow\ \dfrac{BN}{BM}=\dfrac{BH}{BA}$

$\Leftrightarrow\ BN.BA=BH.BM\ \color{red}{(3)}$

$\hspace{0.65cm}\ \text{Xét}\ \triangle BHP\ \text{và}\ \triangle BCM\ \text{có:}$

$\hspace{0.65cm}\ \widehat{B}\ \text{chung}$

$\hspace{0.65cm}\ \widehat{BPH}=\widehat{BMC}\ (=90^\circ)$

$\Rightarrow\ \triangle BHP\ \backsim\ \triangle BCM\ \text{(g - g)}$

$\Rightarrow\ \dfrac{BH}{BC}=\dfrac{BP}{BM}$

$\Leftrightarrow\ BH.BM=BP.BC\ \color{red}{(4)}$ 

$\hspace{0.65cm}\ \text{Từ}\ \color{red}{(3)}\ \text{và}\ \color{red}{(4)}\ \Rightarrow\ BN.BA=BH.BM=BP.BC\ \text{(đpcm)}$