MathematicsWhich of the following statement (s) is/ are true?

Which of the following statement (s) is/ are true?


  1. A
        Two chords of a circle equidistant from the center are equal
  2. B
        Equal chords in a circle subtend equal angles at the center
  3. C
        Angle in a semicircle is a right angle
  4. D
        All of the above 

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    Solution:

    Given are some statements and we need to which is true.
    Radii of both circles are the same and two chords are equidistant from the center so by Pythagoras theorem, chords have to be equal.
    Since the chords are equal, so their distance from the center will also be equal, and hence congruent triangles will form always and so the chords will always subtend equal angles at the center.
    Also, the angle in a semicircle is a right angle.
    Hence, option 1, 2, 3 is true.
    Therefore, option 4 is correct.
     
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