Giải thích các bước giải:
Ta có $AD$ là phân giác góc $A, DK\perp AB, DM\perp AC$
$\to DK=DM$
$\to AK=AM, AD\perp KM$
$\to S_{AKDM}=2S_{AKD}$
$\to \dfrac12AD\cdot KM=2\cdot \dfrac12\cdot AK\cdot KD$
$\to AD\cdot KM=2\cdot AK\cdot KD$
$\to \dfrac{KM}{AD}=2\cdot\dfrac{ AK}{AD}\cdot \dfrac{KD}{AD}$
$\to \dfrac{KM}{AD}=2\cdot\cos\widehat{KAD}\cdot \sin\widehat{KAD}$
$\to \dfrac{KM}{AD}=2\cdot\cos\dfrac{\alpha}{2}\cdot \sin\dfrac{\alpha}{2}$
$\to \dfrac{KM}{AD}=\sin(2\cdot \dfrac{\alpha}{2})=\sin\alpha$
$\to KM=AD\sin\alpha$