Question

在△ABC中,BC=18cm,AC=13cm,AB=17cm,它的内切圆分别和BC,AC,AB切于点D,E,F,求AF,

Answer 1

根据切线的性质,AE=AF,BF=BD,CD=CE,

设AE=x,BD=y,CE=z,

x+y=17,(1)

y+z=18,(2)

x+z=13,(3),

(1)+(2)+(3)式,

x+y+z=24,(4)

(4)-(1)式,

z=7,

(4)-(2)式,

x=6,

(4)-(3)式,

y=11,

∴则AF=AE=6,

BD=11,

CE=7.