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Omni-MATH / Let P be a parabola with focus F and directrix ℓ. A line through F intersects P at two points A and B. Let D and C be the feet of the altitudes from A and B onto ℓ, respectively. G…

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problem

Let P\mathcal{P} be a parabola with focus FF and directrix ℓ\ell. A line through FF intersects P\mathcal{P} at two points AA and BB. Let DD and CC be the feet of the altitudes from AA and BB onto ℓ\ell, respectively. Given that AB=20AB=20 and CD=14CD=14, compute the area of ABCDABCD.
Plain-text mathematical notation (without MathML)
Let P be a parabola with focus F and directrix ℓ. A line through F intersects P at two points A and B. Let D and C be the feet of the altitudes from A and B onto ℓ, respectively. Given that AB=20 and CD=14, compute the area of ABCD.
Original LaTeX notation
Let $\mathcal{P}$ be a parabola with focus $F$ and directrix $\ell$. A line through $F$ intersects $\mathcal{P}$ at two points $A$ and $B$. Let $D$ and $C$ be the feet of the altitudes from $A$ and $B$ onto $\ell$, respectively. Given that $AB=20$ and $CD=14$, compute the area of $ABCD$.

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Source and history

task_id
7fe5cb2a-971c-5913-8c68-4a42bc3f2a01
task_key
test--7fe5cb2a-971c-5913-8c68-4a42bc3f2a01
task_revision_id
1
config / split
/ test

Official source

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