Matematické Fórum

stuart clark · 08. 12. 2018 15:41

$PQRS$ is a convex quadrilateral with $3,4,5$ and $6$ points marked on its sides $PQ,QR,RS$ and $SP$ respectively.

Triangles are formed using these $18$ 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

check_drummer · 08. 12. 2018 20:42

↑ 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...

vanok · 08. 12. 2018 21:11 — Editoval vanok (08. 12. 2018 21:12)

FHi ↑ stuart clark:,
The vertices of the triangles searched are selected in three sides of the quadrilateral $PQRS$ .
So the number of triangles with vertices on side is
3.4.5+3.4.6+3.5.6+4.5.6=...

stuart clark · 09. 12. 2018 13:14

↑ check_drummer: actually question written in that language.

↑ vanok: can you please explain me in detail. Thanks

vanok · 09. 12. 2018 13:38

↑ stuart clark:,
For example,
The number of triangles with vertices on side $PQ,QR,RS$ :
3 possibilities of vertices on side $PQ$
4 possibilities of vertices on side $QR$
5 possibilities of vertices on side $RS$ ,
so you have 3.4.5 such triangles.
.... ( you have 3 others cases)

stuart clark · 17. 12. 2018 16:57

Thanks ↑ vanok:

Matematické Fórum

#1 08. 12. 2018 15:41

number of quadrilateral

#2 08. 12. 2018 20:42

Re: number of quadrilateral

#3 08. 12. 2018 21:11 — Editoval vanok (08. 12. 2018 21:12)

Re: number of quadrilateral

#4 09. 12. 2018 13:14

Re: number of quadrilateral

#5 09. 12. 2018 13:38

Re: number of quadrilateral

#6 17. 12. 2018 16:57

Re: number of quadrilateral

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