A Line Through the Center

★ 7/10plane geometry Law of Sines trigonometry Extrema

Problem

An equilateral triangle $ABC$ has side length $1$ and center $O$ . A line through $O$ meets the sides $AB$ and $AC$ at $M$ and $N$ respectively. Find the range of possible values of

\frac{1}{OM^2} + \frac{1}{ON^2}.

Answer

Solution

Difficulty	7/10
Topics	plane geometry, Law of Sines, trigonometry, Extrema

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