MathematicsState true or false.The angle bisector of any angle of a triangle and perpendicular bisector of the opposite side if intersect, they will intersect on the circumcircle of the triangle.

State true or false.


The angle bisector of any angle of a triangle and perpendicular bisector of the opposite side if intersect, they will intersect on the circumcircle of the triangle.


  1. A
      True
  2. B
      False 

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    Solution:

    Given that, an angle bisector of any angle of a triangle and perpendicular bisector of the opposite side.
    Making figure using given data. Joining BP and CP   .
    Since angles in the same segment are equal, thus ∠BAP=∠BCP  .
    AP is bisector of ∠A  . So,
    Using equation 1 and equation 2,  ∠BCP=∠PBC   Since, the angles subtended by the chords of a circle at the center are equal, then the chords are equal.
    So, BP= CP   And P   is perpendicular on BC.   Hence, given statement is true option 1 is correct.
     
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