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Symmetry - hints need please

  1. Nov 14, 2005 #1
    Right I have been given the following problem and cannot resolve it. I have had an attempt but without much success. Could anyone help me with this exercise, please?

    A cyclic hexagon is a hexagon whose vertices all lie on the circumference of a circle.

    The vertices of a cyclic hexagon are labelled in order A to F. Prove that the sum of the interior angles at A, C and E is equal to the sum of the interior angles at B, D and F.

    Generalise (concisely) to other cyclic polygons?

    My answer so far

    I drew the hexagon and labelled angle A is formed of angles f and a, B of a and b, C, b and c, D of c and d, E of d and e and F of e and f.

    And wrote from the drawing we can see that

    a+f+b+c+e+d = a+f+b+c+e+d

    But I don't think this is really a clear way of proving is it? Do I need to use angles dimensions and sides?

    Where do I go from here basically?
  2. jcsd
  3. Nov 14, 2005 #2


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    Science Advisor
    Homework Helper

    Use Theorem 2 from here.
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