勾股定理:
AD=√(BD^2-AB^2)=√(12^2-10^2)=2√11
∵BD是角平分线
∴DE=AD=2√11
二倍角公式:
cos∠ABC=2(cos∠DBA)^2-1=2*(10/12)^2-1=7/18
∴BC=AB/cos∠ABC=10/(7/18)=180/7
∴CE=BC-BE=BC-AB=180/7-10=110/7
∵∠CDE=∠ABC
∴cos∠CDE=cos∠ABC=7/18
∴CD=DE/cos∠CDE=2√11/(7/18)=36√11/7
∴△DEC周长s
=CD+DE+CE
=36√11/7+2√11+110/7
=(50√11+110)/7