Giải thích các bước giải:
a.Ta có : $MQ//NP\to \widehat{KNP}=\widehat{IKQ},\widehat{KQI}=\widehat{KPN}$
$\to\Delta KQI\sim\Delta PKN(g.g)$
Lại có $QP//MN\to \widehat{QKI}=\widehat{MNI},\widehat{NMI}=\widehat{KQI}$
$\to\Delta QKI\sim\Delta MNI(g.g)$
b.Ta có $MN=10\to QP=10\to KP=10-QK=6$
Do $QK//MN, QI//NP$
$\to \dfrac{QI}{MQ}=\dfrac{KI}{NK}=\dfrac{QK}{MN}=\dfrac{4}{6}=\dfrac{2}{3}$
$\to QI=\dfrac23MQ=8\to MI=MQ+QI=20$
c.Ta có $\widehat{MIN}=\widehat{KNP}(MI//NP),\widehat{MNI}=\widehat{NKP}(MN//QP)$
$\to\Delta MNI\sim\Delta PKN(g.g)$
$\to\dfrac{MN}{PK}=\dfrac{MI}{PN}=\dfrac{MI}{MQ}(MQ=PN)$
$\to MI.PK=MN.MQ$
