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      Question

      Two circles of radii 8 cm and 3 cm have their centers 15

      cm apart. What is the length of the common internal tangent? 
      A 12 cm Correct Answer Incorrect Answer
      B 13 cm Correct Answer Incorrect Answer
      C 14 cm Correct Answer Incorrect Answer
      D 15 cm Correct Answer Incorrect Answer

      Solution

      The length of the common internal tangent is given by √(d² - (r₁ - r₂)²), where d is the distance between the centers, r₁ and r₂ are the radii of the circles. Substituting the values, √(15² - (8 - 3)²) = √(225 - 25) = √200 = 14.14 ≈ 14 cm. Correct answer: c) 14 cm

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