Two circles having equal radius intersect each other such that each passes through the centre of the other. Length of the common chord is 24 cm. Then what will be the diameter or each circle?

$16\sqrt{3}$ cm

According to the diagram,

AD = DB

Let,

O1O2 = 2x

Again O1A = O2A = 2x (Radius of the circle)

\(\angle\)ADO1 = \({90}^\circ\)

O1D = O2D = \(\frac{2x}{2}\) = x

12 = √(\( {4x }^{2 } \) - \( {x }^{2 } \))

x = 4√3

Radius = 2x =8√3

Diameter = 8√3 x 2 = 16√3

Therefore, the diameter is 16√3 cm.