Giải thích các bước giải:

a.Xét $\Delta AMC,\Delta ABN$ có:

$AM=AB$

$\widehat{MAC}=90^o+\hat A=\widehat{BAN}$

$AC=AN$

$\to \Delta AMC=\Delta ABN(c.g.c)$

$\to CM=BN$

b.Gọi $CM\cap AB=D, CM\cap BN=E$

Từ a $\to \widehat{AMC}=\widehat{ABN}$

$\to \widehat{AMD}=\widehat{DBE}$

$\to \widehat{DEB}=180^o-\widehat{DBE}-\widehat{EDB}=180^o-\widehat{AMD}-\widehat{ADM}=\widehat{DAM}=90^o$

$\to BN\perp MC$