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Omni-MATH / Square ABCD is inscribed in circle ω with radius 10. Four additional squares are drawn inside ω but outside ABCD such that the lengths of their diagonals are as large as possible. …

Problem

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problem

Square ABCDABCD is inscribed in circle ω\omega with radius 10. Four additional squares are drawn inside ω\omega but outside ABCDABCD such that the lengths of their diagonals are as large as possible. A sixth square is drawn by connecting the centers of the four aforementioned small squares. Find the area of the sixth square.
Plain-text mathematical notation (without MathML)
Square ABCD is inscribed in circle ω with radius 10. Four additional squares are drawn inside ω but outside ABCD such that the lengths of their diagonals are as large as possible. A sixth square is drawn by connecting the centers of the four aforementioned small squares. Find the area of the sixth square.
Original LaTeX notation
Square \(ABCD\) is inscribed in circle \(\omega\) with radius 10. Four additional squares are drawn inside \(\omega\) but outside \(ABCD\) such that the lengths of their diagonals are as large as possible. A sixth square is drawn by connecting the centers of the four aforementioned small squares. Find the area of the sixth square.

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Source and history

task_id
be1dbf3f-59d7-57cd-92e3-6470d927da02
task_key
test--be1dbf3f-59d7-57cd-92e3-6470d927da02
task_revision_id
1
config / split
/ test

Official source

initial import