(1)如图,由已知ac平分∠bad得
∠1=∠2
∵bc⊥ac,cd⊥ad,且AB=18,AC=12
∴AD/AC=cos∠1 AC/AB=cos∠2
∴AD/AC=AC/AB
AD=AC*AC/AB=12*12/18=8
(2)
从题意中得知:△ABC和△ACD为直角三角形,∠ACB=∠ADC=90°,
且AC平分∠BAD,则∠BAC=∠DAC
则△ABC∽△ADC
又因为若DE⊥AC,CF⊥AB,则∠AED=∠AFC=90°,且∠FAC=∠EAD(角平分线)
则△AFC∽△ADC,且△ABC∽△ADC∽△AFC∽△ADC
则DE/CF=AC/AB=12/18=2/3