# Tough geometry problem about triangles, proof

QuantumQuest
Gold Member
Sorry, I can't find the other triangle of interest :( also what can I do with the first relation?
For the second question, is it better to have ## \cos(60 + \alpha) ## or expand it? If you do, you'll have ## \cos ## or ## \sin ## separately. Think about that.
For the first question, you have used the three external equilateral triangles and the inner that you want to prove equilateral. There is exactly one triangle, that you have not used yet.

EDIT: Don't forget your goal. You must somehow end up with a relation that concludes about sides of the inner triangle.

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Are you referring to ABC?

QuantumQuest
Gold Member
Are you referring to ABC?
That's right. This has an interesting angle regarding your previous calculations and some interesting sides. But what can you do on this triangle? You have again to connect angles with sides, so you know what to do by now. Your goal is substituting things into the first relation you initially wrote. But there is something more, regarding ABC, that you can use.

Cozma Alex
Ok, thanks for the help, Im gonna use the sine and the cosine theorem on ABC to find something
I can go alone by now, thanks again for the patience
:)

QuantumQuest