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Omni-MATH / An equiangular hexagon has side lengths 1,1,a,1,1,a in that order. Given that there exists a circle that intersects the hexagon at 12 distinct points, we have M<a<N for some real n…

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problem

An equiangular hexagon has side lengths 1,1,a,1,1,a1,1, a, 1,1, a in that order. Given that there exists a circle that intersects the hexagon at 12 distinct points, we have M<a<NM<a<N for some real numbers MM and NN. Determine the minimum possible value of the ratio NM\frac{N}{M}.
Plain-text mathematical notation (without MathML)
An equiangular hexagon has side lengths 1,1,a,1,1,a in that order. Given that there exists a circle that intersects the hexagon at 12 distinct points, we have M<a<N for some real numbers M and N. Determine the minimum possible value of the ratio (N)/(M).
Original LaTeX notation
An equiangular hexagon has side lengths $1,1, a, 1,1, a$ in that order. Given that there exists a circle that intersects the hexagon at 12 distinct points, we have $M<a<N$ for some real numbers $M$ and $N$. Determine the minimum possible value of the ratio $\frac{N}{M}$.

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task_id
8b557c13-ed8d-5faa-b965-ce86067a971c
task_key
test--8b557c13-ed8d-5faa-b965-ce86067a971c
task_revision_id
1
config / split
/ test

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