In the following figure, there are two circles that touch each other externally. The radius of the first circle with centre P is 25 cm. The radius of the second circle with centre Q is 4 cm. Find the length of their direct common tangent AB.

F1 SSC Arbaz 6-10-23 D24

Figure is not to scale and is only for representational purpose

This question was previously asked in
SSC CGL 2023 Tier-I Official Paper (Held On: 25 Jul 2023 Shift 1)
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  1. 21 cm
  2. 18 cm
  3. 20 cm
  4. 22 cm

Answer (Detailed Solution Below)

Option 3 : 20 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:

Radius of large circle = 25 cm

Radius of small circle = 4 cm

Formula used:

Direct common tangent = 2 × √(R × r)

Calculation:

Direct common tangent (AB) = 2 × √(R × r)

⇒ 2 × √(25 × 4)

⇒ 2 × 10 = 20 cm

∴ The correct answer is 20 cm. 

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