Ta có $\left\{ \begin{array}{l}CD\bot AB\\CD\bot BC\end{array} \right.\Rightarrow CD\bot (ABC)\Rightarrow CD\bot AC$. $\Rightarrow \Delta ACD$ vuông tại C. $\begin{array}{l}\Rightarrow A{{D}^{2}}=A{{C}^{2}}+C{{D}^{2}}=A{{B}^{2}}+B{{C}^{2}}+C{{D}^{2}}={{a}^{2}}+{{b}^{2}}+{{c}^{2}}\\\Rightarrow AD=\sqrt{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}\end{array}$
