MathematicsState true or false.If ABC is an equilateral triangle inscribed in a circle and P be any point on the minor arc BC which does not coincide with B or C, then PA is angle bisector of ∠BPC.

State true or false.


If ABC is an equilateral triangle inscribed in a circle and P be any point on the minor arc BC which does not coincide with B or C, then PA is angle bisector of ∠BPC.


  1. A
      True
  2. B
       False  

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    Solution:

    Given that if ABC is an equilateral triangle inscribed in a circle and P be any point on the minor arc BC which does not coincide with B or C, then PA is angle bisector of ∠BPC.
    Joining PB and PC   in the figure below.
    We know in equilateral triangle ABC   all three sides have the same length, and all angles are as 60 °  .
    So, ∠3+∠4= 60 °  .
    Also, we know angles on the same line segment are equal,
    In line segment AB, ∠1+∠4= 60 °  .
    In line segment AC   ∠2+∠3= 60 °  .
    So,  ∠1+∠2= 60 °  .
    Thus, PA   is angle bisector of ∠BPC   and the statement is true.
    Hence option 1 is true.
     
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