连接AE、CE
∵DE是AC的垂直平分线
∴AE=CE
AD=CD=1/2AC=1/2√(AB²+BC²)=1/2√(5²+12²)=13/2
AE²=AB²+BE²=5²+BE²=25+BE²
CE²=DE²+CD²=DE²+(13/2)²=DE²+169/4
BE=BC-CE=12-√(DE²+169/4)
AE²=CE²
25+BE²=DE²+169/4
25+(12-√(DE²+169/4))²=DE²+169/4
100+4(144+DE²+169/4-24√(DE²+169/4))=4DE²+169
100+576+4DE²+169-96√(DE²+169/4)=4DE²+169
96√(DE²+169/4)=676
√(DE²+169/4)=169/24
DE²+169/4=169²/24²
DE²=169/4(169/144-1)=169/4*25/144
DE=13/2*5/12=65/24