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\(Mỗi đường thẳng cắt 100 đường thẳng còn lại nên tạo nên 100 giao điểm. Có 101 đường thẳng nên có 101. 100 giao điểm, nhưng mỗi giao điểm đã được tính hai lần nên chỉ có : 101. 100 : 2 = 5050 (giao điểm).\)
Cũng câu hỏi như vậy với 2012 đường thẳng.
Để làm được bài này ta cần thêm điều kiện "6 đường thẳng đôi một cắt nhau" và không có 3 đường thẳng nào đồng quy.
1. Bài làm :
Chọn 1 đường thẳng cắt 19 đg thẳng còn lại tạo ra 19 giao điểm .
Có 20 đường thẳng nên có 20.19 giao điểm nhưng mỗi giao điểm lại đc tính 2 lần nên => có :
20.19 : 2 = 190 [giao điểm ]
Vậy có 190 giao điểm .
1. Bài làm :
Chọn một điểm , nối điểm đó với 29 điểm còn lại tạo ra 29 đường thẳng .
Có 30 điểm thì sẽ có 30.29 đường thẳng nhưng mỗi đường thẳng được tính 2 lần nên => có :
30.29:2=435[ đường thẳng ]
Vậy có 435 đường thẳng
Số giao điểm của chúng là :
\(\frac{2006.2005}{2}=2011015\) (giao điểm)
Hai đường thẳng nào cũng cắt nhau nên mỗi đường thẳng cắt 2005 đường còn lại ta được 2005 giao điểm
Có 2006 đường thẳng => có 2006.2005 giao điểm
Trong đó, mỗi giao điểm đều được tính 2 lần
Vậy số giao điểm tạo thành là: 2006.2005 /2 = ... giao điểm
Hai đường thẳng nào cũng cắt nhau nên mỗi đường thẳng cắt 2005 đường còn lại ta được 2005 giao điểm
Có 2006 đường thẳng => có 2006.2005 giao điểm
Trong đó, mỗi giao điểm đều được tính 2 lần
Vậy số giao điểm tạo thành là: 2006.2005 /2 = ... giao điểm
có 2011015 đường thẳng
2011015 chắt 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có 2011015 đường thẳng
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
Chọn 1 trong 2006 đường thẳng, đường thẳng này kết hợp với 2005 đường thẳng còn lại ta được 2005.2006( giao điểm).
Nhưng như vậy thì mỗi giao diểm được tính 2 lần.
Do vậy thực sự chỉ có 2005.2006:2=2011015(giao điểm)
emnhungkhohieu