How many triangles?
We can see that the picture looks like a "THE".
We have 13 points in total. So the total combinations between them is:
Ç13,3 = 286
However, we want only those that form triangles, so we have to subtract all combinations that do not form triangles, that is, the combinations in which the points are COLINARY. We have 3 situations where this happens:
In the "left leg" of "THE"we have 6 collinear points that cannot be combined because they do not form triangles.
In the "right leg" of "THE"we have the same situation.
And in the middle we have 4 collinear points that can't be combined either.
We have to subtract this 3 situations from the total. So the number of triangles that can be formed is:
Ç13,3 - Ç6,3 - Ç6,3 - Ç4,3 = 286 - 20 - 20 - 4 = 242
Therefore they can be formed 242 distinct triangles !!!
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