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Omni-MATH / Let A₁A₂…A₆ be a regular hexagon with side length 11√(3), and let B₁B₂…B₆ be another regular hexagon completely inside A₁A₂…A₆ such that for all i∈{1,2,…,5},A_(i)A_(i+1) is paralle…

Problem

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problem

Let A1A2…A6A_{1} A_{2} \ldots A_{6} be a regular hexagon with side length 11311 \sqrt{3}, and let B1B2…B6B_{1} B_{2} \ldots B_{6} be another regular hexagon completely inside A1A2…A6A_{1} A_{2} \ldots A_{6} such that for all i∈{1,2,…,5},AiAi+1i \in\{1,2, \ldots, 5\}, A_{i} A_{i+1} is parallel to BiBi+1B_{i} B_{i+1}. Suppose that the distance between lines A1A2A_{1} A_{2} and B1B2B_{1} B_{2} is 7 , the distance between lines A2A3A_{2} A_{3} and B2B3B_{2} B_{3} is 3 , and the distance between lines A3A4A_{3} A_{4} and B3B4B_{3} B_{4} is 8 . Compute the side length of B1B2…B6B_{1} B_{2} \ldots B_{6}.
Plain-text mathematical notation (without MathML)
Let A₁A₂…A₆ be a regular hexagon with side length 11√(3), and let B₁B₂…B₆ be another regular hexagon completely inside A₁A₂…A₆ such that for all i∈{1,2,…,5},A_(i)A_(i+1) is parallel to B_(i)B_(i+1). Suppose that the distance between lines A₁A₂ and B₁B₂ is 7 , the distance between lines A₂A₃ and B₂B₃ is 3 , and the distance between lines A₃A₄ and B₃B₄ is 8 . Compute the side length of B₁B₂…B₆.
Original LaTeX notation
Let $A_{1} A_{2} \ldots A_{6}$ be a regular hexagon with side length $11 \sqrt{3}$, and let $B_{1} B_{2} \ldots B_{6}$ be another regular hexagon completely inside $A_{1} A_{2} \ldots A_{6}$ such that for all $i \in\{1,2, \ldots, 5\}, A_{i} A_{i+1}$ is parallel to $B_{i} B_{i+1}$. Suppose that the distance between lines $A_{1} A_{2}$ and $B_{1} B_{2}$ is 7 , the distance between lines $A_{2} A_{3}$ and $B_{2} B_{3}$ is 3 , and the distance between lines $A_{3} A_{4}$ and $B_{3} B_{4}$ is 8 . Compute the side length of $B_{1} B_{2} \ldots B_{6}$.

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Source and history

task_id
81dce4be-1892-5436-ae8d-f5fd0f4aa1ee
task_key
test--81dce4be-1892-5436-ae8d-f5fd0f4aa1ee
task_revision_id
1
config / split
/ test

Official source

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