MathematicsA chord of a circle is equal to the radius of the circle. The angle subtended by the chords at a point on the minor arc and also at a point on the major arc is ____o.

A chord of a circle is equal to the radius of the circle. The angle subtended by the chords at a point on the minor arc and also at a point on the major arc is ____o.


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    Solution:

    A chord of a circle is equal to the radius of the circle. The angle subtended by the chords at a point on the minor arc and also at a point on the major arc is 30o.
    It is given that chord of a circle is equal to its radius.
    Let O be the centre of the circle, OA be the radius and AB be the chord, as shown in the figure.
     A chord of a circle is equal to the radius of the circle. Find the angle  subtended by the chord at a point on the minor arc and also at a pointThe angle subtended by the chords at a point on the minor arc and also at a point on the major arc is 30o.
    In ∆AOB,
    Radius OA = Chord AB.
      AO=OB=BA   So, ∆AOB is an equilateral triangle.
    AOB= 60 °  
    By degree measure theorem,
      AOB =2ACB 60 ° =2ACB ACB = 60 ° 2 ACB = 30 °  
    Opposite angles of cyclic quadrilateral are supplementary.
    ACB+ADB = 180 ° 30 ° +ADB = 180 ° ADB = 180 ° 30 ° ADB = 150 °  
    Therefore, angle by chord AB at minor arc = 150°.
    Angle by chord AB at major arc = 30°.
    Hence, the required answer is 30o.
     
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