MathematicsState true or false.If two chords AB and CD of a circle AYDZBWCX intersect at right angles (below Fig.), then arc CXA + arc DZB = arc AYD + arc BWC =2 semi-circle

State true or false.


If two chords AB and CD of a circle AYDZBWCX intersect at right angles (below Fig.), then arc CXA + arc DZB = arc AYD + arc BWC =2 semi-circle


Diagram, pie chart Description automatically generated

  1. A
    True
  2. B
    False 

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    Solution:

    Given: Two chords AB and CD   of a circle AYDZBWCX   intersect at right angles
    Joining CA,AD,DB and BC,   then circle and, let the chords intersect at O.   Diagram, pie chart Description automatically generatedThe, angle made by chord AC   is ∠CBA   and angle made by chord BD   is ∠BCD.   So, from the above figure:
    ∠CBA+∠BCD= 180 ° −∠COB   ∠CBA+∠BCD= 180 ° − 90 °   ∠CBA+∠BCD= 90 °   Thus, angle made in a semicircle is 90 °   and  Similarly, .
    Thus, statement is false, .
    Hence, option 2 is correct.
     
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