Giải thích các bước giải:

a.Xét $\Delta MEP,\Delta NPQ$ có:

Chung $\hat P$

$\widehat{MEP}=\widehat{NQP}(=90^o)$

$\to \Delta MEP\sim\Delta NQP(g.g)$

b.Xét $\Delta MEP,\Delta EPK$ có:

Chung $\hat P$

$\widehat{MEP}=\widehat{PKE}(=90^o)$

$\to \Delta MEP\sim\Delta EKP(g.g)$

$\to \dfrac{EP}{KP}=\dfrac{MP}{EP}$

$\to PE^2=PM.PK=36$

$\to PE=6$

c.Xét $\Delta MEK,\Delta MEP$ có:

Chung $\hat M$

$\widehat{MKE}=\widehat{MEP}(=90^o)$

$\to \Delta MKE\sim\Delta MEP(g.g)$

$\to \dfrac{MK}{ME}=\dfrac{ME}{MP}$

$\to ME^2=MK.MP$

$\to \dfrac{EP^2}{EM^2}=\dfrac{PK.PM}{MK.MP}=\dfrac{KP}{KM}$

Vì $KI//ME(\perp NP)$

$\to \dfrac{IP}{IE}=\dfrac{KP}{KM}$

$\to \dfrac{EP^2}{EM^2}=\dfrac{IP}{IE}$