Specific triangle, symmetral of angle proof

Question

In triangle $ABC$, angle $\gamma = 120$. Prove that $|\overline{CC'}|=\tfrac{ab}{a+b}$, where $\overline{CC'}$ is symmetral of angle $\gamma$ inside triangle. Look at image.

Triangle

I can't use areas, becuase we haven't learned them yet. Our teacher says that the trick is to extend $\overline{CC'}$ to have equilateral triangle. But I don't know where to go from that.

Your teacher on one hand gives a suggestion, but on the other hand, he/she has also added an distraction too -- i.e. "c". — Mick, Nov 27 '14 at 18:46

score 0 · Answer 1 · answered Nov 27 '14 at 17:09

0

i will take your teachers suggestion and extend $CC^\prime$ up to $D$ so that the triangle $BCD$ is an equilateral triangle.

what can you conclude about the lines $BD$ and $AC?$

what about the triangles $ACC^\prime$ and $BDC^\prime?$

i will leave the rest for you to finish off.

answered Nov 27 '14 at 17:09

abel

29,170

Thanks. Now it seems easy, but I wasn't able to figure it out by myself – user195929 Nov 27 '14 at 18:00
@user195929, you are welcome. glad to be of some help. – abel Nov 27 '14 at 18:06

Specific triangle, symmetral of angle proof

1 Answers1