There are two circles touching each other externally. The radius of the first circle with centre O is 12 cm. The radius of the second circle with centre A is 5 cm. Find the length of their common tangent touching the two circles at points P and Q.

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SSC CHSL Exam 2024 Tier-I Official Paper (Held On: 11 Jul, 2024 Shift 3)
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  1. \(5\sqrt{14}\) cm
  2. \(4\sqrt{15}\) cm
  3. \(5\sqrt{41}\) cm
  4. 14√5 cm

Answer (Detailed Solution Below)

Option 2 : \(4\sqrt{15}\) cm
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SSC CHSL Exam 2023 Tier-I Official Paper (Held On: 02 Aug 2023 Shift 1)
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100 Questions 200 Marks 60 Mins

Detailed Solution

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Concept used:

If two circles touch each other externally, then the length of their common tangent = 2√r1r2 , where r1 and r2 are radius

Calculation:

F1 Savira SSC 23-9-24 D5

Radius of the first circle (r1) = 12 

Radius of the second circle (r2) = 5

Then, according to the question,

the length of their common tangent BC

= 2√(12 × 5)

= 2√60

= 2 ×√(4 × 15)

= 4√15 cm

∴ The correct answer is 4√15 cm.

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