MathematicsState true or false.A circle has radius 2    cm. It is divided into two segments by a chord of length 2 cm. Then angle subtended by the chord at a point in the major segment is 55º.

State true or false.


A circle has radius 2    cm. It is divided into two segments by a chord of length 2 cm. Then angle subtended by the chord at a point in the major segment is 55º.


  1. A
    True
  2. B
    False 

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    Solution:

    Given that a circle has radius 2    cm. It is divided into two segments by a chord of length 2 cm. Then angle subtended by the chord at a point in the major segment is 55º.
    Creating figure using given data:
    We have BC=2  .
    Now squaring on both sides of BC=2  .
    BC 2 = 2 2 BC 2 4=2+2 BC 2 =( 2 ) 2 +( 2 ) 2   BC 2 = OB 2 + OC 2   So, in triangle BOC we have,
    BC 2 = OB 2 + OC 2   Thus ∠BOC= 90 °   (By Converse of Pythagoras theorem).
    So, arcBC   subtends ∠BOC   from the center O and angle ∠BAC   at left segment of the circle,
    Since the angle subtended by an arc at the center is double the angle subtended by it at any point on the left part of the circle, therefore ∠BOC=2∠BAC  .
    ∠BOC=2∠BAC   90 ° =2∠BAC  
    90 ° 2 =∠BAC   45 ° =∠BAC   ∠BAC= 45 °   As the angle subtended by the chord at a point in major segment is 45 °  , thus statement is false.
    Hence, option 2 is correct.
     

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