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      Question

      Now a chord of a circle is such that AB = 10 cm. If the

      diameter of the circle is 20 cm, then the angle subtended by the chord at the center is.
      A 45° Correct Answer Incorrect Answer
      B 30° Correct Answer Incorrect Answer
      C 60° Correct Answer Incorrect Answer
      D 90° Correct Answer Incorrect Answer

      Solution

      Radius of circle= 10 cm Length of chord= 10 cm OA =10 =AB =OB now, draw a perpendicular on the chord from the center of the circle which divides the chord into two equal parts. In AAOC OA =10 =AB =OB AD=DB= 5 cm cosec = AD /AO =5 /10 = 1/ 2 = cos60° θ = 60° Hence, the angle subtended by the chord is 60°.

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