Giải thích các bước giải:
Ta có : $MN//PQ\to\dfrac{KM}{KP}=\dfrac{KN}{KQ}=\dfrac{NM}{PQ}=\dfrac49$
$\to KM=\dfrac49KP, KQ=\dfrac94KN$
Vì $MP\perp QN\to KM^2+KN^2=MN^2=16$
Ta có : $\widehat{MKN}=\widehat{MKQ}=90^o, \widehat{KMN}=\widehat{MQK}(+\widehat{QMK}=90^o)$
$\to \Delta MKN\sim\Delta QKM(g.g)$
$\to \dfrac{KM}{KN}=\dfrac{KQ}{KM}\to KM^2=KQ.KN=\dfrac94KN^2$
$\to KM^2+KN^2=\dfrac94KN^2+KN^2=\dfrac{13}{4}KN^2=16$
$\to KN=\dfrac{8\sqrt{13}}{13}$
$\to KM=\dfrac{12\sqrt{13}}{13}$