Two equal circles of radius 18 cm intersect each other, such that each passes through the centre of the other. The length of the common chord is _________.

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SSC CGL 2023 Tier-I Official Paper (Held On: 24 Jul 2023 Shift 4)
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  1.  cm
  2.  cm
  3.  cm

Answer (Detailed Solution Below)

Option 1 :  cm
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Detailed Solution

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Given:

The radius of the circles is 18 cm

Calculation:

According to the diagram,

AD = DB

O1O2 = 18

Again O1A = O2A = 18 [Radius of the circle]

∠ADO1 = 90°

O1D = O2D = 9

AD = √(324 - 81)

⇒ (9√3) 

AB = 2 × (9√3) = 18√3 = 6√27

∴ The length of the common chord is 6√27 cm.

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