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Ptolemy's Theorem and Cyclic Quadrilateral

  1. Feb 5, 2012 #1
    1. The problem statement, all variables and given/known data
    In cyclic quadrilateral ABCD with diagonals intersecting at E, we have AB=5, BC=10, BE=7, and CD=6. Find CE.

    2. Relevant equations
    Ptolemy's Theorem: The product of the measures of its diagonals is equal to the sum of the products of the measures of the pairs of opposite sides.

    3. The attempt at a solution
    I drew the picture and that's as far as I got.

    Attached Files:

    • pic.png
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  2. jcsd
  3. Feb 10, 2012 #2
    Hint : First prove that ΔDEC is similar to ΔAEB by axiom AAA. To prove them similar , you have to apply theorem related to angles subtended by same segment or arc on circumference. Do you know what does that theorem state ?
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