1973 IMO Problems/Problem 1


Point $O$ lies on line $g;$ $\overrightarrow{OP_1}, \overrightarrow{OP_2},\cdots, \overrightarrow{OP_n}$ are unit vectors such that points $P_1, P_2, \cdots, P_n$ all lie in a plane containing $g$ and on one side of $g.$ Prove that if $n$ is odd, \[\left|\overrightarrow{OP_1}+\overrightarrow{OP_2}+\cdots+ \overrightarrow{OP_n}\right|\ge1.\] Here $\left|\overrightarrow{OM}\right|$ denotes the length of vector $\overrightarrow{OM}.$


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See Also

1973 IMO (Problems) • Resources
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First Question
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Problem 2
All IMO Problems and Solutions
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