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AP EAMCET2010MathematicsCircle

The length of the common chord of the circles of radii 15 and 20, whose centres are 25 unit of distance apart, is

Options

  1. A12
  2. B16
  3. C24
  4. D25

Correct answer

C. 24

Step-by-step solution

Given, r₁=15 unit r₂=20 unit C₁ C₂=25 unit Let A C₂ D= Then, in right angled triangle A D C₂ , A D=r₂ A D r₂ = ...(i) Now, in right angled triangle A D C₁A D=r₁ (90- ) A D r₁ = ...(ii) On squaring and adding Eqs. (i) and (ii), we get A D^2 [ 1 r₁^2 + 1 r₂^2 ]=1 A D^2 ( r₁^2+r₂^2 r₁^2 r₂^2 )=1 A D^2= r₁^2 r₂^2 r₁^2+r₂^2 A D^2= 225 400 225+400 A D= 15 20 25 =12 Thus, length of common chord =2 A D=2 12=24 unit

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