Giải thích các bước giải:

a.Xét $\Delta OAB,\Delta MEB$ có:

CHung $\hat B$

$\hat O=\hat M(=90^o)$

$\to \Delta OAB\sim\Delta MEB(g.g)$

b.Xét $\Delta AMN,\Delta AOB$ có:

Chung $\hat A$

$\hat M=\hat O(=90^o)$

$\to \Delta AMN\sim\Delta AOB(g.g)$

$\to \dfrac{AM}{AO}=\dfrac{AN}{AB}$

$\to AM.AB=AN.AO$

c.Xét $\Delta AMO,\Delta ANB$ có:

Chung $\hat A$

$ \dfrac{AM}{AO}=\dfrac{AN}{AB}$

$\to \Delta AMO\sim\Delta ANB(c.g.c)$

$\to \widehat{AOM}=\widehat{ABN}$

Xét $\Delta NOB,\Delta NAF$ có:

$\hat O=\hat F(=90^o)$

$\widehat{ONB}=\widehat{FNA}$

$\to \Delta NOB\sim\Delta NFA(g.g)$

$\to \dfrac{NO}{NF}=\dfrac{NB}{NA}$

$\to \Delta NOF\sim\Delta NBA(c.g.c)$

$\to \widehat{NOF}=\widehat{NBA}=\widehat{AOM}$

$\to AO$ là phân giác $\widehat{MOF}$