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A dot is marked at each vertex of a triangle \(ABC\) . Then \(2,3\) and \(7\) more dots are marked on the sides \(AB,BC\) and \(CA\) respectively. How many triangles have their vertices at these dots?

 Nov 26, 2022
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You can divide into casework:

(1) One vertex on AB, one vertex on AC, A.

(2) One vertex on BC, one vertex on BA, B

(3) One vertex on CA, one vertex on CB, C

 

Adding these up, gives you 120 + 80 + 150 = 350.

 Nov 27, 2022

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