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In article <5hs7fa$4p7@opus.vcn.bc.ca>, landmark@vcn.bc.ca (Scott Phung) wrote:

> 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.

Yes, they do. It's not too hard to prove... especially if you know the
theorem saying this:

If A and B are two points on the circle, O its center and C1 and C2 points
on the circle such that C1 is on the longer of the two arcs between A and B
and C2 is on the shorter one (if AB is a diameter, then it's irrelevant
which arc they're on), the following holds:

<AOB = 2*<AC1B
360 - <AOB = 2*<AC2B

From this it immediatelly follows that 2*<AC1B + 2*<AC2B = 360; also note
that AC1BC2 is a cyclic quadrilateral... which completes the proof that sum
of opposite angles in a cyclic quadrilateral is 180.

Hth,

meeroh

-- 
Miroslav Jurisic | meeroh@mit.edu | http://www.mit.edu/people/meeroh/
MIT Information Systems (Mac development) | Athena On-Line Consulting
Lt. Commander Meeroh Ambellus, ATS TrekMUSH  (ats.trekmush.org:1701)

"It's not hatred that's important; it's the desire to anihilate." [101
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