🚀 go-pugleaf

Brian McCague <brian@mccague.demon.co.uk> wrote:
BM> In article <5hnv2g$95s@opus.vcn.bc.ca>, Scott Phung <landmark@vcn.bc.ca>
BM> writes
BM> >Here's a math problem that's been on my mind:
BM> >
BM> >  Suppose I have a circle with a radius r.  Then into it is
BM> >inscribed a cyclic quadrilateral.  Is the area of this cyclic
BM> >quadrilateral = 2r^2?  I know that if the cyclic quadrilateral
BM> >was a square, then the area of the square = 2r^2.
BM> >
BM> >  More Generally, if a polygon is inscribed into a circle with
BM> >a radius r, would the area of the polygon inscribed = area of
BM> >regular polygon inscribed?
BM> >
BM> >  Also, does the center of the circle lie on any of the two
BM> >diagonals of the cyclic quadrilateral?
BM> >
BM> >  Can anyone confirm the any of above?
BM> >
BM> >
BM> Consider a quadrilateral formed by four points that are very close
BM> together on the circle's circumference.  It follows that the answer to
BM> the above questions is 'no'.
BM> --
BM> Brian McCague

But does the angles diagonally opposite of each other add to 180?

A ......... D
   .     .
 B  ..... C

Does <B + <D = 180
 and <A + <C = 180?

Yes, it's easy to image four points close together, but do these
four points satisfy the above?  Perhaps you can provide an
example.

If it adds to 180, my mistake and I will be beleive that
this area is smaller than that of a inscribed square.

Thanks,
Scott Phung.

--

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