# Number of right angled triangles formed by vertices of a 14-gon

Here's a question that I found on the website of International Kangaroo Maths Contest. The question goes like this:

What is the total number of right angled triangles that can be formed by joining the vertices of a regular 14-gon?

Correct Answer: The correct answer as given on the website is $$84$$.

What I did:

First of all, I calculated the total number off triangles (right angled or not) that can be formed by using the vertices of a regular 14-gon that is $$^{14}C_3=364$$.

However, I can't figure out how to count which ones of these $$364$$ triangles are right angled. Please help me in this regard.

Thanks for the attention!

We have $$7$$ diameters and for each one we have 6 point on each side. So we have $$7\cdot 12=84$$ right triangles.