Prove that triangle ABC is isosceles
Triangle ABC has the following properties: there is an interior point P such that angle PAB = 10 degrees, angle PBA = 20 degrees, angle PCA = 30 degrees and angle PAC = 40 degrees. Prove that triangle ABC is isosceles.
Very difficult problem don't know where to start.
Any help appreciated.
Re: Prove that triangle ABC is isosceles
Sorry to open the old thread, but a user has just posted this problem recently, and I think i should give a link to the solution, as the problem is both famous, interesting and not wrong...
the link does not seem to work:
consider and we know , hence
now we have to use the trigonometric version of ceva's theorem:
=> [#using product-sum formula]
so as , we can write or
hence ,therefore triangle ABC is isosceles