* 這是角A!! Orz 為什麼出不來
\angle{A}
\angle CAD+\angle BAC=90{}^\circ =\angle ABF+\angle BAC\Rightarrow \angle CAD=\angle ABF\Rightarrow \triangle DEA \sim \triangle AFB
令
\overline{AB}=5t,\ \overline{BF}=3t,\ \overline{AF}=4t\Rightarrow \overline{CF}=3+7-4t=10-4t
利用
{{\overline{AB}}^{2}}+{{\overline{AD}}^{2}}={{\overline{BC}}^{2}}+{{\overline{CD}}^{2}}
\Rightarrow {{\left( 5t \right)}^{2}}+{{5}^{2}}=\underbrace{{{\left( 3t \right)}^{2}}+{{\left( 10-4t \right)}^{2}}}_{{{\overline{BC}}^{2}}={{\overline{BF}}^{2}}+{{\overline{CF}}^{2}}}+{{\left( \sqrt{65} \right)}^{2}}
可解得
t=\frac{\ 7\ }{4} \Rightarrow \overline{BF}=3t=\frac{\ 21\ }{4}
