MathematicsThe sum of opposite sides of a cyclic quadrilateral is π?

The sum of opposite sides of a cyclic quadrilateral is π?

  1. A
    sum of opposite angles of a Cyclic Quadrilateral is π 
  2. B
    sum of angles of a Cyclic Quadrilateral is π
  3. C
    sum of opposite angles of a Cyclic  is π
  4. D
    sum of opposite Cyclic Quadrilateral is π 

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    Solution:

    Let  be the given cyclic quadrilateral of a circle with centre at  .
    Now construct a cyclic quadrilateral by joining the diagonal of the quadrilateral and naming the angles as shown in the figure:
    seoWe have to prove that sum of the angles of opposite sides are 180∘
    By angle sum property of Quadrilateral
    …………………………………….(1)
    By the property of angles in the same segment are equal
    From equation (1) we have
      Using the above relations, we get
    From the figure clearly, we have
    Similarly, we can write
    Hence the sum of opposite angles of a Cyclic Quadrilateral is π.
    So, option 1 is correct.
     
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