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Omni-MATH / Let ABCDEFGH be an equilateral octagon with angle A cong angle C cong angle E cong angle G and angle B cong angle D cong angle F cong ∠H. If the area of ABCDEFGH is three times the…

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problem

Let ABCDEFGHA B C D E F G H be an equilateral octagon with $\angle A \cong \angle C \cong \angle E \cong \angle G$ and $\angle B \cong \angle D \cong \angle F \cong$ ∠H\angle H. If the area of ABCDEFGHA B C D E F G H is three times the area of ACEGA C E G, then sinB\sin B can be written as mn\frac{m}{n}, where m,nm, n are positive integers and gcd(m,n)=1\operatorname{gcd}(m, n)=1. Find 100m+n100 m+n.
Plain-text mathematical notation (without MathML)
Let ABCDEFGH be an equilateral octagon with $\angle A \cong \angle C \cong \angle E \cong \angle G$ and $\angle B \cong \angle D \cong \angle F \cong$ ∠H. If the area of ABCDEFGH is three times the area of ACEG, then sinB can be written as (m)/(n), where m,n are positive integers and gcd(m,n)=1. Find 100m+n.
Original LaTeX notation
Let $A B C D E F G H$ be an equilateral octagon with $\angle A \cong \angle C \cong \angle E \cong \angle G$ and $\angle B \cong \angle D \cong \angle F \cong$ $\angle H$. If the area of $A B C D E F G H$ is three times the area of $A C E G$, then $\sin B$ can be written as $\frac{m}{n}$, where $m, n$ are positive integers and $\operatorname{gcd}(m, n)=1$. Find $100 m+n$.

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Source and history

task_id
7dd05509-fde0-5abd-b492-ebb6670a68c6
task_key
test--7dd05509-fde0-5abd-b492-ebb6670a68c6
task_revision_id
1
config / split
/ test

Official source

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