Giải thích các bước giải:

a.Xét $\Delta AID,\Delta CIN$ có:

$\widehat{IAD}=\widehat{ICN}$ vì $AD//BC$

$\widehat{AID}=\widehat{CIN}$

$\to \Delta AID\sim\Delta CIN(g.g)$

b.Xét $\Delta ADM,\Delta CDN$ có:

$\widehat{DAM}=\widehat{DAB}=\widehat{DCB}=\widehat{DCN}$

$\widehat{AMD}=\widehat{NDC}$ vì $AB//CD$

$\to \Delta ADM\sim\Delta CND(g.g)$

c.Từ câu b $\to \dfrac{AM}{CD}=\dfrac{AD}{CN}$

$\to AM\cdot CN=AD\cdot CD=AD\cdot AB$

d.Ta có:  $AD//BC, AB//CD$

$\to\dfrac{IM}{ID}=\dfrac{IA}{IC}=\dfrac{ID}{IN}$

$\to ID^2=IM\cdot IN$