Explanation:

Let there be 2 circles with centre O₁ and O

AB is the common chord

Since both passes through the center of each other as shown in figure

So O₁O is the radius of both

Let O₁O = r = AO₁ = AO AX = AB / 2 = 5√3 cm (since OX perpendicular to chord bisects it)

AOO₁ forms an equilateral triangle with on side = radius = r Sin 60 = √3/2 = AX / AO = 5√3/r

So r = 10cm

So diameter = 20 cm