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MATH / A chord of a circle is perpendicular to a radius at the midpoint of the radius.…

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problem

A chord of a circle is perpendicular to a radius at the midpoint of the radius. The ratio of the area of the larger of the two regions into which the chord divides the circle to the smaller can be expressed in the form $\displaystyle {{a\pi+b\sqrt{c}}\over{d\pi-e\sqrt{f}}}$, where aa, bb, cc, dd, ee, and ff are positive integers, aa and ee are relatively prime, and neither cc nor ff is divisible by the square of any prime. Find the remainder when the product a⋅b⋅c⋅d⋅e⋅fa\cdot b\cdot c\cdot d\cdot e\cdot f is divided by 1000.
Plain-text mathematical notation (without MathML)
A chord of a circle is perpendicular to a radius at the midpoint of the radius. The ratio of the area of the larger of the two regions into which the chord divides the circle to the smaller can be expressed in the form $\displaystyle
{{a\pi+b\sqrt{c}}\over{d\pi-e\sqrt{f}}}$, where a, b, c, d, e, and f are positive integers, a and e are relatively prime, and neither c nor f is divisible by the square of any prime.  Find the remainder when the product a⋅b⋅c⋅d⋅e⋅f is divided by 1000.
Original LaTeX notation
A chord of a circle is perpendicular to a radius at the midpoint of the radius. The ratio of the area of the larger of the two regions into which the chord divides the circle to the smaller can be expressed in the form $\displaystyle
{{a\pi+b\sqrt{c}}\over{d\pi-e\sqrt{f}}}$, where $a$, $b$, $c$, $d$, $e$, and $f$ are positive integers, $a$ and $e$ are relatively prime, and neither $c$ nor $f$ is divisible by the square of any prime.  Find the remainder when the product $a\cdot
b\cdot c\cdot d\cdot e\cdot f$ is divided by 1000.

level

Level 5

type

Geometry

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Source and history

task_id
30245e8a-d9ce-5427-8eff-65d481e6a3a4
task_key
geometry--test--30245e8a-d9ce-5427-8eff-65d481e6a3a4
task_revision_id
1
config / split
geometry / test

Official source

initial import