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is a convex quadrilateral with and points marked on its sides and respectively.
Triangles are formed using these points and the original vertices of a quadrilateral.
Then number of such triangle that do not have any side or part of a side common with the quadrialeral are
↑ stuart clark:
Hi, it seems that all triangles are part of the quadrilateral so the answer is 0. But maybe you mean not quadrilateral but its circumference, do you? If it is so what do you mean by "part" - when one point is common with that circumference is it part of it or not? May be you mean part that is of nonzero length...
FHi ↑ stuart clark:,
The vertices of the triangles searched are selected in three sides of the quadrilateral .
So the number of triangles with vertices on side is
↑ stuart clark:,
The number of triangles with vertices on side :
3 possibilities of vertices on side
4 possibilities of vertices on side
5 possibilities of vertices on side ,
so you have 3.4.5 such triangles.
.... ( you have 3 others cases)