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NTA Abhyas JEE Main2020MathematicsCirclePractice

Two circles with centers at A and B touch each other externally at T . Let BD is the tangent at D and T C is a common tangent. If A T has length 3 units and B T has length 2 units, then the length (in units) of C B is

Options

  1. A4 3
  2. B5 2
  3. C5 3
  4. D7 4

Correct answer

B. 5 2

Step-by-step solution

From the diagram, In ∆ A B D ,   sin ⁡ B = 3 5 ,   cos ⁡ B = 4 5 In ∆ B T C ,   cos ⁡ B = T B B C = 4 5 ∴ B C = 5 2 units

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