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NTA Abhyas JEE Main2020MathematicsCirclePractice

A circle C 1 has radius 2 units and a circle C 2 has radius 3 units. The distance between the centres of C 1 and C 2 is 7 units. If two lines, one tangent to both circles and the other passing through the center of both circles, intersect at point P which lies between the centers of C 1 and C 2 , then the distance between P and the centre of C 2 is

Options

  1. A9 4 units
  2. B7 3 units
  3. C21 5 units
  4. D14 5 units

Correct answer

C. 21 5 units

Step-by-step solution

Since △ O 1 P T 1 ~ △ O 2 P T 2 , ∴ 2 3 = x 7 - x 3 x = 14 - 2 x x = 14 5 ⇒ P O 2 = 7 - 14 5 = 21 5 units

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