MathematicsIf △ABC  is circumscribing a circle in the figure. The length of AB is

If ABC  is circumscribing a circle in the figure. The length of AB is


  1. A
         12 cm  
  2. B
         13 cm  
  3. C
         9 cm  
  4. D
         14 cm   

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    Solution:

    Given that ABC is circumscribing a circle.
    From figure, BC = 6cm, CD = 4cm and AC = 12cm.
    We know that the length of tangents drawn from an external point to the circle are equal.
    Therefore,
    BC = BF = 6cm
    CD = CE = 4cm
    AF = AE
    Let AE = x cm
    Now, AC = AE + CE
    12 = x + 4
    x = 12 – 4
    x = 8 cm
    Therefore, AE = AF = 8cm.
    Now,
    AB = AF + CF
    AB = 8 + 6
    AB = 12 cm
    Hence the length of AB is 12 cm.
    Therefore, option 1 is correct.
     
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