Triangles?

Look it up. It was in some kind of puzzle championship.

Yeah , there are 56 triangles. You can count them like this : firstly take the 2 biggest triangles made by the triples of outer vertices and see that they are intersecting in 6 other vertices since any two edges of one triangle is intersected by an edge of the other triangle forming 6 smaller triangles at the angles which means that until now there are 2+6=8 triangles. Now at this next step there will be counted the number of triangles generated by one of the lines that connects vertices of the biggest triangles. Firstly observe that since this edge connects the vertices of the 2 biggest triangles it is included in both and therefore it affects both of them. This edge divides the smaller and the biggest triangle we thus far obtained into 2 making therefore 2+2=4 triangles per triangle or 4 * 2=8 triangles in total and also two triangles by uniting the 2 vertices it connects giving a total of 8+2=10 triangles in total per line and since every line behaves the same and are 3 lines we have a total of 30 triangles. Count the compound triangles made by the intersection of 3 lines we draw. Since they intersect in the two biggest triangles at the center they generate 3 smaller triangles each made from two of this edges inside each of the biggest triangles and for every such included triangle we have that it is divided in 2 by the other edge that doesn't form a triangle therefore being 3+6=9 included triangles per big triangle and 9 * 2=18 triangles in total. And now finally it can be count the results which it can be sure by the fact that the triangles used are different and we counted correctly at every step the number of triangles generated that are the total this being 8 + 30 + 18 = 56 triangles in total in the figure. This would be some sort of improvised solution yet , it would be nicer to find some sort of law or formula by which for such constructions it can be derived the number which maybe I or someone else will post as an alternative and pretty sure a better and less confusing solution.