证明：∵$CE\perp AB，$$BF\perp AC，$∴$∠DEB = ∠DF C = 90°$
在$\triangle DEB$和$\triangle DF C$中
$\begin {cases}∠DEB=∠DF C\\∠EDB=∠F DC\\BD = CD\end {cases}$
∴$\triangle DEB≌\triangle DF C(\mathrm {AAS})，$∴$DE = DF$
又∵$DE\perp AB，$$DF\perp AC$
∴点$D$在$∠BAC$的平分线上
