Charles Link's latest activity

I am working on that now. In principle I should be able to generalize it.

It's a lot of extra algebra. I did it for the solution with ## \cos{\theta} ## that I solved above, and without a doubt, it will work...

Thanks! I managed to do it using my formula above as the starting point. Basically it involved untangling the trig functions into an...

@bob012345 You definitely get the correct numerical answer with your method, but I had no success in using your formula to get an...

The answer is no. If it is not contained in a circle, the 3rd angle can be chosen arbitrarily.

I did not see this problem until last night but I solved it at least numerically by using the chord formula and knowing the sum of the...

For real solutions, the longest chord can't be larger than the sum of the other three. Meanwhile, thank you @bob012345 =Bob V., you...

Makes it too easy. It is worth the effort to derive these results. The math skills of this latest generation seem to be falling apart.

Try again. ## \cos(\pi-\theta)=-\cos{\theta} ##. Once you have ## \cos{\theta} ##, you have 3 points: ## (0,0) ##, ##(2,0) ##, and...

absurd "coincidence": when I "solved " it (completely wrong) by confusing tangent with cosine, I got sqrt(11/4); and the actual answer...

The two opposite angles adding to ## \pi ## radians (when a 4 sided polygon is inscribed in a circle) makes it readily workable. I may...

I even solved the problem now in the OP, expressing the ## \cos{\theta} ## in terms of the sides of the polygon, and getting an answer...

Working it with the polygon on the outside I think is much more difficult, but you will also find a circle that works, if I'm not...

The lack of response on this is disappointing. I thought it was one of the better math problems I had seen in the last couple of...

The law of cosines is basically the Pythagorean theorem when applied to triangles that don't have the 90 degree angle.