MathematicsState true or false.If the perpendicular bisector of a chord AB of a circle PXAQBY intersects the circle at P and Q, Then PXA ≅ Arc PYB.

State true or false.


If the perpendicular bisector of a chord AB of a circle PXAQBY intersects the circle at P and Q, Then PXA ≅ Arc PYB.


  1. A
    True
  2. B
    False 

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    Solution:

    Given that, the perpendicular bisector of a chord AB   of a circle PXAQBY   intersects the circle at P and Q.
     Considering triangle APM and triangle BPM,
    The perpendicular bisector PQ   bisect chord AB  .
    So, AM=MB  .
    ∠AMP=∠BMP= 90 °               (Common side)
    By SAS congruence rule, ΔAPM≅ΔBMP  .
    Therefore, by CPCT,
    AP=BP  
    Since two chords of a circle are equal, their corresponding arcs are congruent, thus.
    Therefore, the statement is true, option 1 is correct.
     
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