Two equal circles of radius 8 cm intersect each other in such a way that each passes through the centre of the other. The length of the common chord is:

Correct option is A

Solution:

According to diagram,

AD = BD

​$$O_1O_2 = 8$$​​

$$O_1A = O_2A$$​ = 8 (Radius of the circle)

​$$\angle ADO_1 = 90^\circ$$​​

​$$O_1D = O_2D = 4$$​​

AD = $$\sqrt{64 - 16} = \sqrt{48} = 4\sqrt{3}$$​​

AB = 2 × AD = $$2 \times 4\sqrt{3} = 8\sqrt{3} \text{ cm}$$

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