I have to solve a math problem written in English. The wording is the following :

" In triangle ABC, the angle bisector of angle A intersects line BC at D and the circumference of triangle ABC at E. The external angle-bisector of angle A intersects line BC at F and the circumference of triangle ABC at G. Prove that DG⊥EF. "

I am quite confused regarding the meaning of "circumference". How could an angle bisector intersect the circumference of a triangle?!

So, I am wondering this because I have read that perimeter was a synonym..

Could you please enlighten me? Thanks!

  • 1
    $\begingroup$ I think it means the circumference of the circumcircle of the triangle $ABC$. $\endgroup$ – Peter Huxford Oct 31 '14 at 23:33
  • $\begingroup$ Oh ok, you must be right. Thank you for the clarification. $\endgroup$ – Albert Oct 31 '14 at 23:41
  • $\begingroup$ I agree the question is worded a bit poorly: as far as I'm aware triangle's don't have circumferences, only circles do. At least, I've never seen it used in that way before. $\endgroup$ – Peter Huxford Oct 31 '14 at 23:43

You can draw a circle with a circumference that goes through the three vertices of the triangle, it means this circle.


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