Giải thích các bước giải:
a.Ta có :
$\widehat{DKM}=\widehat{EPM}$
$\widehat{DME}=\widehat{DKM}\to \widehat{DMK}+\widehat{EMP}=\widehat{DMK}+\widehat{KDM}$
$\to\widehat{EMP}=\widehat{MDK}\to\Delta MKD\sim\Delta EPM(g.g)$
$\to\dfrac{KD}{PM}=\dfrac{MK}{EP}\to KD.PE=PM.MK=\dfrac{1}{4}KP^2$
b.Ta có : $\widehat{DME}=\widehat{DKM}$
Theo câu a $\dfrac{KD}{PM}=\dfrac{MD}{ME}$
$\to \dfrac{KD}{KM}=\dfrac{MD}{ME}$
Mà $\widehat{DME}=\widehat{DKM}\to\Delta DKM\sim\Delta DME(c.g.c)\to \widehat{KDM}=\widehat{MDE}$
$\to DM$ là phân giác $\widehat{KDE}$