延长BC，作∠BAE=90，交BC延长线于E这样AC平分∠BAE，由角平分线定理得到AB/AE=BC/CE而易证AB/AE=BD/AD这样有BD/AD=BC/CECE=BC*AD/BD=(5/3)ADED=CE+CD=(5/3)AD+4而根据射影定理得到AD^2=BD*DEAD^2=6[(5/3)AD+4]解得AD=12
