In a triangle $\bigtriangleup ABC$,a,b,c are its sides ,A,B $\xi\;$ C are its angles, if $\cot A,\cot B\;\xi\;\cot C$ are in AP , the a,b, and c are in which progression?

Question

$(a)\;AP\qquad(b)\;GP\qquad(c)\;HP\qquad(d)\;No\;such\;relationship\;exists$