- #1

- 493

- 8

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?

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?