Question

△ABC中,D为BC的中点,G为AD的中点,过点G任作一直线MN分别交AB,AC,于M,N两点，若AM=XAB,AN=YAC,

问：1/x+1/y是否为定值

Answer 1

PG=AG-AP=1/2AD-mAB=1/4(AB+AC)-mAB=(1/4-M)AB+1/4AC
QG=AG-AQ=1/2AD-nAC=1/4(AB+AC)-nAC=(1/4-n)AC+1/4AB
PG QG 共线

(1/4-m)AB+1/4AC=t1/4-nAC+1/4AB]
1/4-m=t/4
1/4=t(1/4-n)
两式相除消去t
m+n=4mn
1/m+1/n=4