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The figure below is a segment of a circle centre O radius r units.CM is the perpendicular bisector of AB. 
figure showing segment of a circle
Given that CM=1cm and AB=2√3cm,

  1. calculate the radius of the circle centre O from which the segment was cut 
  2. calculate the angle that chord AB subtends at the centre of the circle 
  3. hence calculate
    1. the length of arc ACB 
    2. the area of the segment AMBC

1 Answer

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  1. radius of centre O calculations
    r2=(r − 1)+ (√3)2    
    r2 =r− 2r + 1 + 3     
    2r = 4
    r=2cm    
  2. Cos θ = ½ = 0.5
          θ =60º                   
    Angle at centre =120°   
  3.  
    1.  120/360 × 2 × 22/7 ×2 =4.190       
    2. 120/360 × 22/7 × 22 − ½ ×2sin 120   
      =4.190 − 1.7321 = 2.4579                     
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