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Omni-MATH / Let Ω be a circle of radius 8 centered at point O, and let M be a point on Ω. Let S be the set of points P such that P is contained within Ω, or such that there exists some rectang…

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problem

Let Ω\Omega be a circle of radius 8 centered at point OO, and let MM be a point on Ω\Omega. Let SS be the set of points PP such that PP is contained within Ω\Omega, or such that there exists some rectangle ABCDA B C D containing PP whose center is on Ω\Omega with AB=4,BC=5A B=4, B C=5, and BC‖OMB C \| O M. Find the area of SS.
Plain-text mathematical notation (without MathML)
Let Ω be a circle of radius 8 centered at point O, and let M be a point on Ω. Let S be the set of points P such that P is contained within Ω, or such that there exists some rectangle ABCD containing P whose center is on Ω with AB=4,BC=5, and BC‖OM. Find the area of S.
Original LaTeX notation
Let $\Omega$ be a circle of radius 8 centered at point $O$, and let $M$ be a point on $\Omega$. Let $S$ be the set of points $P$ such that $P$ is contained within $\Omega$, or such that there exists some rectangle $A B C D$ containing $P$ whose center is on $\Omega$ with $A B=4, B C=5$, and $B C \| O M$. Find the area of $S$.

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Source and history

task_id
3d1b813f-19b4-57eb-8dcf-c6f17a411731
task_key
test--3d1b813f-19b4-57eb-8dcf-c6f17a411731
task_revision_id
1
config / split
/ test

Official source

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