如图,点B,C在线段AD上,且AB:BC=AD:CD.求证:1/AB+1/AD=2/AC

如图,点B,C在线段AD上,且AB:BC=AD:CD.求证:1/AB+1/AD=2/AC
如图,点B,C在线段AD上,且AB:BC=AD:CD.求证:1/AB+1/AD=2/AC

如图,点B,C在线段AD上,且AB:BC=AD:CD.求证:1/AB+1/AD=2/AC
设AB=1,BC=x,CD=y,则AC=x+1,AD=x+y+1
∵AB:BC=AD:CD
∴BC*AD=AB*CD
即x*(x+y+1)=y
∴1/(x+y+1)=x/y,1+x/y=2/(1+x)
∴1+1/(x+y+1)=2/(1+x)
即1/AB+1/AD=2/AC