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If two parallel chords of a circle, having diameter 4 units, lie on the opposite sides of the centre and subtend angles cos -1 (1/7) and sec -1 (7) at the centre respectively, then the distance between these chords, is : 16/7 8/(7 1/2 ) 8/7 4/7

If two parallel chords of a circle, having diameter 4 units, lie on the opposite sides of the centre and subtend angles cos-1 (1/7) and sec-1 (7) at the centre respectively, then the distance between these chords, is :
  1. 16/7
  2. 8/(71/2)  
  3. 8/7
  4. 4/7

Grade:11

1 Answers

Arun
25750 Points
3 years ago
distance between chords
 
= Radius Cos(subtended angle/2) by chord1 +  Radius Cos(subtended angle/2) by chord 2
 
Radius = Diameter /2 = 4/2 = 2
 
= 2 Cos (θ₁/2) + 2Cos(θ₂/2)
 
θ₁ = Cos⁻¹(1/7) => Cosθ₁ = 1/7
 
θ₂ = Sec⁻¹7 => Secθ₂ = 7 => 1/Cosθ₂ = 7 => Cosθ₂ = 1/7
 
Applying Cos2θ = 2Cos²θ - 1 => Cos²θ =  (1 + cos2θ)/2
 
Putting θ  = θ₁/2
 
Cos²(θ₁/2) = ( 1 + 1/7)/2 = 4/4
 
=> Cos(θ₁/2) = 2/√7
 
Putting θ  = θ₂/2
 
Cos²(θ₂/2) = ( 1 + 1/7)/2 = 4/7
 
=> Cos(θ₁/2) = 2/√7
 
2 Cos (θ₁/2) + 2Cos(θ₂/2) = 2 *2/√7 + 2 * 2/√7
 
= 4/√7  + 4/√7
 
= 8/√7
 
 

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