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Omni-MATH / Trapezoid ABCD is inscribed in the parabola y=x² such that A=(a,a²),B=(b,b²), C=(−b,b²), and D=(−a,a²) for some positive reals a,b with a>b. If AD+BC=AB+CD, and AB=(3)/(4), what is…

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problem

Trapezoid ABCDA B C D is inscribed in the parabola y=x2y=x^{2} such that A=(a,a2),B=(b,b2)A=\left(a, a^{2}\right), B=\left(b, b^{2}\right), C=(−b,b2)C=\left(-b, b^{2}\right), and D=(−a,a2)D=\left(-a, a^{2}\right) for some positive reals a,ba, b with a>ba>b. If AD+BC=AB+CDA D+B C=A B+C D, and AB=34A B=\frac{3}{4}, what is aa?
Plain-text mathematical notation (without MathML)
Trapezoid ABCD is inscribed in the parabola y=x² such that A=(a,a²),B=(b,b²), C=(−b,b²), and D=(−a,a²) for some positive reals a,b with a>b. If AD+BC=AB+CD, and AB=(3)/(4), what is a?
Original LaTeX notation
Trapezoid $A B C D$ is inscribed in the parabola $y=x^{2}$ such that $A=\left(a, a^{2}\right), B=\left(b, b^{2}\right)$, $C=\left(-b, b^{2}\right)$, and $D=\left(-a, a^{2}\right)$ for some positive reals $a, b$ with $a>b$. If $A D+B C=A B+C D$, and $A B=\frac{3}{4}$, what is $a$?

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Source and history

task_id
c5aa8bb7-b36c-5846-ab34-9f33d5870533
task_key
test--c5aa8bb7-b36c-5846-ab34-9f33d5870533
task_revision_id
1
config / split
/ test

Official source

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