14.（★★★）如图，在$\triangle ABC$中，$BD$平分$\angle ABC$，$BD\perp AC$于点$D$，点$F$在$AC$上，
点$E$在$AB$的延长线上，连接$EF$交$BC$于点$G$，且$\angle ABC = 2\angle E$。
(1)试问：$EF$与$AC$有怎样的位置关系？请说明理由.
(2)若$\angle E = 40^{\circ}$，请求出$\angle C$的度数。
答案：(1) $EF\perp AC$. 理由如下： $BD$ 平分 $\angle ABC$，
$\therefore\angle ABC = 2\angle ABD$.
$\because\angle ABC = 2\angle E$,
$\therefore\angle ABD=\angle E$. $\therefore BD// EF$.
$\therefore\angle ADB=\angle AFE$.
$\because BD\perp AC$,
$\therefore\angle ADB = 90^{\circ}$. $\therefore\angle AFE = 90^{\circ}$.
$\therefore EF\perp AC$.
(2) $\because\angle E = 40^{\circ}$, $\angle ABC = 2\angle E$,
$\therefore\angle ABC = 80^{\circ}$.
$\because BD// EF$,
$\therefore\angle BCE=\angle CBD=\frac{1}{2}\angle ABC=\angle E = 40^{\circ}$.
$\because\angle CGF = 40^{\circ}$.
由(1)可知，$\angle AFE = 90^{\circ}$,
$\therefore\angle GFC = 90^{\circ}$.
$\therefore\angle C = 90^{\circ}-\angle CGF = 50^{\circ}$.
