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Construct all possible chords connecting the two vertices of a decagon. Given that no three of these chords intersect at one point, how many triangles with vertices as the interior intersections are there?


The answer is 210.

Alan Yan by Alan Yan , 20, USA

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1 solution

Alan Yan
Sep 21, 2015

Notice that with any 6 6 vertices of the decagon, you can construct one triangle. Therefore the total number of triangles is ( 10 6 ) = 210 {10 \choose 6} = \boxed{210}

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