ABC成等差数列,A+C=2B=π-B,3B=π,B=π/3,
abc成等比数列,b^2=ac,
由余弦定理,b^2=a^2+c^2-2ac*cosπ/3=a^2+c^2-ac=ac,a^2+c^2-2ac=0,(a-c)^2=0,a=c,又B=π/3,则A=C=π/3=B,a=b=c,三角形ABC为等边三角形.