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In the figure below A, B, C and D are points on the circumference of the circle, centre 0, A tangent to the circle at A intersects chord CD produced at E. Line AB is parallel to line EC. Angle AED = 45° and angle ABD = 40°.

  1. Calculate the size of
    • <ADB. 
    • <OCD 
  2. Given that ED = 3.5 cm and DC = 4.9 cm, calculate correct to 1 decimal place: 
    • the length of the tangent AE. 
    • the radius of the circle. 

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    • <ADB = 45
    • <OCD = 35
  1. 8.4 x 3.5=AE2
    • AE=±5.422
      ∴ AE = 5.422 ≈ 5.4
      r = 2.45  
           cos 35
      = 2.991
      ≈ 3.0 cm

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