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Omni-MATH / Chords (AB)¯ and (CD)¯ of circle ω intersect at E such that AE=8,BE=2,CD=10, and ∠AEC=90^(∘). Let R be a rectangle inside ω with sides parallel to (AB)¯ and (CD)¯, such that no poi…

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problem

Chords AB¯\overline{A B} and CD¯\overline{C D} of circle ω\omega intersect at EE such that AE=8,BE=2,CD=10A E=8, B E=2, C D=10, and ∠AEC=90∘\angle A E C=90^{\circ}. Let RR be a rectangle inside ω\omega with sides parallel to AB¯\overline{A B} and CD¯\overline{C D}, such that no point in the interior of RR lies on AB¯,CD¯\overline{A B}, \overline{C D}, or the boundary of ω\omega. What is the maximum possible area of RR?
Plain-text mathematical notation (without MathML)
Chords (AB)¯ and (CD)¯ of circle ω intersect at E such that AE=8,BE=2,CD=10, and ∠AEC=90^(∘). Let R be a rectangle inside ω with sides parallel to (AB)¯ and (CD)¯, such that no point in the interior of R lies on (AB)¯,(CD)¯, or the boundary of ω. What is the maximum possible area of R?
Original LaTeX notation
Chords $\overline{A B}$ and $\overline{C D}$ of circle $\omega$ intersect at $E$ such that $A E=8, B E=2, C D=10$, and $\angle A E C=90^{\circ}$. Let $R$ be a rectangle inside $\omega$ with sides parallel to $\overline{A B}$ and $\overline{C D}$, such that no point in the interior of $R$ lies on $\overline{A B}, \overline{C D}$, or the boundary of $\omega$. What is the maximum possible area of $R$?

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Source and history

task_id
777a0b9c-1f3b-5a32-a9c2-36aeea22d896
task_key
test--777a0b9c-1f3b-5a32-a9c2-36aeea22d896
task_revision_id
1
config / split
/ test

Official source

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