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Omni-MATH / Let A₁,A₂,…,A₂₀₁₅ be distinct points on the unit circle with center O. For every two distinct integers i,j, let P_(ij) be the midpoint of A_(i) and A_(j). Find the smallest possibl…

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problem

Let A1,A2,…,A2015A_{1}, A_{2}, \ldots, A_{2015} be distinct points on the unit circle with center OO. For every two distinct integers i,ji, j, let PijP_{i j} be the midpoint of AiA_{i} and AjA_{j}. Find the smallest possible value of ∑1≤i<j≤2015OPij2\sum_{1 \leq i<j \leq 2015} O P_{i j}^{2}.
Plain-text mathematical notation (without MathML)
Let A₁,A₂,…,A₂₀₁₅ be distinct points on the unit circle with center O. For every two distinct integers i,j, let P_(ij) be the midpoint of A_(i) and A_(j). Find the smallest possible value of ∑_(1≤i<j≤2015)OP_(ij)².
Original LaTeX notation
Let $A_{1}, A_{2}, \ldots, A_{2015}$ be distinct points on the unit circle with center $O$. For every two distinct integers $i, j$, let $P_{i j}$ be the midpoint of $A_{i}$ and $A_{j}$. Find the smallest possible value of $\sum_{1 \leq i<j \leq 2015} O P_{i j}^{2}$.

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Source and history

task_id
7bf7ef96-9f19-5dfc-90a6-26b35df08892
task_key
test--7bf7ef96-9f19-5dfc-90a6-26b35df08892
task_revision_id
1
config / split
/ test

Official source

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