1973 IMO Problems/Problem 1
Revision as of 15:15, 17 February 2018 by Durianaops (talk | contribs) (Created page with "==Problem== Point <math>O</math> lies on line <math>g;</math> <math>\overrightarrow{OP_1}, \overrightarrow{OP_2},\cdots, \overrightarrow{OP_n}</math> are unit vectors such tha...")
Problem
Point 
lies on line 
are unit vectors such that points 
all lie in a plane containing 
and on one side of 
Prove that if 
is odd, ![\[\left|\overrightarrow{OP_1}+\overrightarrow{OP_2}+\cdots+ \overrightarrow{OP_n}\right|\ge1.\]](http://latex.artofproblemsolving.com/7/c/2/7c261196979f62bc5b704df4bace1553f2760e4b.png)
Here 
denotes the length of vector 
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See Also
| 1973 IMO (Problems) • Resources | ||
| Preceded by First Question |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 2 |
| All IMO Problems and Solutions | ||
