由ρ=1得x2+y2=1,又∵ρ=2cos(θ+π3)=cosθ-3sinθ,∴ρ2=ρcosθ-3ρsinθ,∴x2+y2?x+3y=0,由x2+y2=1x2+y2?x+3y=0得A(1,0),B(-12,?32),∴AB=