Three circles each of radius 5 cm touch one another. The area (in cm2) subtended between them is:

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SSC CPO 2024 Official Paper-I (Held On: 28 Jun, 2024 Shift 3)
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  1. \(25\left(\sqrt{3}+\frac{\pi}{2}\right) \)
  2. \(25\left(2 \sqrt{3}-\frac{\pi}{2}\right)\)
  3. \(50\left(\sqrt{3}-\frac{\pi}{2}\right) \)
  4. \(25\left(\sqrt{3}-\frac{\pi}{2}\right)\)

Answer (Detailed Solution Below)

Option 4 : \(25\left(\sqrt{3}-\frac{\pi}{2}\right)\)
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Detailed Solution

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Given:

Three circles each of radius 5 cm touch one another.

Formula used:

For three circles touching one another, the area subtended between them is given by:

Area = r2(√3 - π/2)

Where r is the radius of the circles.

Calculations:

Radius (r) = 5 cm

⇒ Area = 52(√3 - π/2)

⇒ Area = 25(√3 - π/2)

∴ The area subtended between the circles is 25(√3 - π/2) cm2.

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