Talk:Law of Cosines/Proof 2

"We need a more general form than Intersecting Chord Theorem, because AC may not be long enough."

Please explain, because I can't make any sense of it. --prime mover (talk) 23:40, 18 May 2013 (UTC)

Sorry yes I get it, if $\angle BAC$ is close to $2 \pi$ and $AC$ is much less than both $AB$ and $AC$, $B$ ends up outside the circle. Okay so in that case you use the Secant Secant Theorem.

Off you go, then, there's a job for you. --prime mover (talk) 23:44, 18 May 2013 (UTC)

It's a bit more complicated than that. If $AB > AC$, then $B$ lies outside the circle. When this is the case, the geometric relationships between different intersection points will depend on whether $\angle ACB$ is acute, right, or obtuse. I don't think the latter will affect the computation, but it will certainly affect the picture. Note: I haven't done this sort of geometry since I was thirteen years old, so my memory of the theorems involved is extremely rusty. My memory of the teacher involved, however, is vivid. She could be very difficult to deal with, and some students lived in terror of her, but she was spectacular at driving students to learn the mental discipline of writing mathematical proofs—sadly, most schools in the U.S. now teach geometry without making students prove anything, which strikes me as a complete waste of time. --Dfeuer (talk) 04:29, 19 May 2013 (UTC)

Is there any point continuing with this proof? There are so many special cases it's getting tedious. If nobody objects I'll just delete the thing and forget it ever existed. --prime mover (talk) 19:25, 19 May 2013 (UTC)

Let me look it over tonight. Or, if you like, move it to my user space without leaving a redirect, so I can put it back where it came from if I am able to make it decent. --Dfeuer (talk) 22:02, 19 May 2013 (UTC)

Feel free to do whatever needs to be done with this - when I was at school they never taught formal geometry, they just went straight to analytic geometry via linear algebra. I taught myself from Euclid many years later. --prime mover (talk) 12:57, 20 May 2013 (UTC)

Didn't euclid show all three of those cases in proving pythagoras's theorem?--G.McSteamy

no --prime mover (talk) 06:28, 27 May 2013 (UTC)