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NTA Abhyas JEE Main2020MathematicsCirclePractice

Let two circles having radii r 1 and r 2 are orthogonal to each other. If the length of their common chord is k times the square root of harmonic mean between the squares of their radii, then k 4 is equal to

Options

  1. A13
  2. B7
  3. C4
  4. D2

Correct answer

C. 4

Step-by-step solution

Area of Δ A B C = 1 2 r 1 r 2 = 1 2 l 2 r 1 2 + r 2 2 ⇒ l = 2 r 1 r 2 r 1 2 + r 2 2 ⇒ l = 2 2 r 1 2 r 2 2 r 1 2 + r 2 2 ⇒ k = 2 ⇒ k 4 = 4

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