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:

This question was previously asked in
SSC CGL 2022 Tier-I Official Paper (Held On : 01 Dec 2022 Shift 4)
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  1. \(8\sqrt3\) cm
  2. \(\sqrt 3\) cm
  3. \(2\sqrt3\) cm
  4. \(4\sqrt3\) cm

Answer (Detailed Solution Below)

Option 1 : \(8\sqrt3\) cm
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PYST 1: SSC CGL - English (Held On : 11 April 2022 Shift 1)
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Detailed Solution

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Given:

The radius of the circles is 8 cm

Calculation:

F1 ArunK Madhuri 11.03.2022 D6

According to the diagram,

AD = DB

O1O2 = 8

Again O1A = O2A = 8 [Radius of the circle]

∠ADO1 = 90°

O1D = O2D = 4

AD = √(64 - 16)

⇒ √48 = 4√3

AB = 2 × 4√3 = 8√3

∴ The length of the common chord is 8√3 cm

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