We know that in an equilateral triangle, all sides are equal in length.

So, AB = BC = CA

Given, O is on the side AB

So, AO < AB

=> AO < AC  ...........1   {since AB = AB}

and CO is the line formed by joining C to the point O and O is no AB

Again, ∠CAO = ∠CBO = ∠ACB         {angles are same in equilateral triangle}

Again given, ∠ACB is split side by side CO

So, ∠ACO < ∠CAO

Again, we know that side opposite to greater angle is longer

So, CO > AO ..........2

Now, from equation 1 and 2, we get

CO must be smaller than AC or AB

Hence, decreasing order is:

AC > CO > AO