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&mdash;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)