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      Question

      In a quadrilateral ABCD, the diagonals AC and BD

      intersect at O. If AO = 8 cm, OC = 12 cm, BO = 6 cm, and OD = 9 cm, find the area of the quadrilateral using the formula for the area of a cyclic quadrilateral.
      A 96 cm² Correct Answer Incorrect Answer
      B 108 cm² Correct Answer Incorrect Answer
      C 150 cm² Correct Answer Incorrect Answer
      D 132 cm² Correct Answer Incorrect Answer

      Solution

      To find the area of quadrilateral ABCD where diagonals AC and BD intersect at O, and the quadrilateral is cyclic or the diagonals are perpendicular, use the formula:

      Compute the diagonals:

      Substitute into the formula:

      The area of the quadrilateral is 150 cm².

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