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Precizati numarul de segmente determinate de 7 puncte coliniare distincte 2 cate 2

Răspuns :

Fie   A1   A2,...,A7   cele   7   puncte
Segmente
[A!A2] [A1 A3]
[A1A4]
.......................
[A1A7]
i   total 6   segmente
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[A2A3]
[A2A4]
......................
[A2A7]
In  total   5  segmente
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[A3A4]
[A3A5]
.........................
[A3A7]
4   seg,ente
..........................
[A4A5]
[A4A6]
[A4A7]
______________
3segmente
[A5A6]
[A5A7]
2segmente
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-A6A7] 1   segment
In  total
1=2+3+...+7=suma  GauSs=7*8/2=28
Fie punctele notate cu litere de la A la G

Segmente: AB, BC,..., FG (sase), AC, BD,..., EG (cinci), AD, BE, CF, DG (patru), AE, BF, CG (trei), AF, BG (doua), AG (unul)

In total 1+2+...+7 = 28 segmente