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NTA Abhyas JEE Main2020MathematicsCirclePractice

Two circles have a direct common tangent with length 36   c m . The shortest distance between these circles is 14   c m . If the radius of the longer circle is 4 times the radius of the smaller circle, then the diameter of the smaller circle (in c m s ) is

Options

  1. A12
  2. B1 0
  3. C14
  4. D18

Correct answer

B. 1 0

Step-by-step solution

From the figure, 9 r 2 + 36 2 = 5 r + 14 2 ⇒ 4 r 2 + 35 r − 25 ⋅ 11 = 0 ⇒ r - 5 4 r + 55 = 0 Hence, r = 5   cms ⇒ 2 r = 10   cms

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