Symmetry - hints need please

  • Thread starter Natasha1
  • Start date
  • #1
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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?
 

Answers and Replies

  • #2
AKG
Science Advisor
Homework Helper
2,565
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Use Theorem 2 from here.
 

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