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Omni-MATH / Side (AB)¯ of △ABC is the diameter of a semicircle, as shown below. If AB=3+√(3),BC=3√(2), and AC=2√(3), then the area of the shaded region can be written as (a+(b+c√(d))π)/(e), wh…

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problem

Side AB¯\overline{A B} of △ABC\triangle A B C is the diameter of a semicircle, as shown below. If AB=3+3,BC=32A B=3+\sqrt{3}, B C=3 \sqrt{2}, and AC=23A C=2 \sqrt{3}, then the area of the shaded region can be written as a+(b+cd)πe\frac{a+(b+c \sqrt{d}) \pi}{e}, where a,b,c,d,ea, b, c, d, e are integers, ee is positive, dd is square-free, and gcd(a,b,c,e)=1\operatorname{gcd}(a, b, c, e)=1. Find 10000a+1000b+100c+10d+e10000 a+1000 b+100 c+10 d+e.
Plain-text mathematical notation (without MathML)
Side (AB)¯ of △ABC is the diameter of a semicircle, as shown below. If AB=3+√(3),BC=3√(2), and AC=2√(3), then the area of the shaded region can be written as (a+(b+c√(d))π)/(e), where a,b,c,d,e are integers, e is positive, d is square-free, and gcd(a,b,c,e)=1. Find 10000a+1000b+100c+10d+e.
Original LaTeX notation
Side $\overline{A B}$ of $\triangle A B C$ is the diameter of a semicircle, as shown below. If $A B=3+\sqrt{3}, B C=3 \sqrt{2}$, and $A C=2 \sqrt{3}$, then the area of the shaded region can be written as $\frac{a+(b+c \sqrt{d}) \pi}{e}$, where $a, b, c, d, e$ are integers, $e$ is positive, $d$ is square-free, and $\operatorname{gcd}(a, b, c, e)=1$. Find $10000 a+1000 b+100 c+10 d+e$.

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task_id
e35279a6-490e-5729-bbc9-49cd775aeba6
task_key
test--e35279a6-490e-5729-bbc9-49cd775aeba6
task_revision_id
1
config / split
/ test

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