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Omni-MATH / ABCDE is a cyclic convex pentagon, and AC=BD=CE.AC and BD intersect at X, and BD and CE intersect at Y. If AX=6,XY=4, and YE=7, then the area of pentagon ABCDE can be written as …

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ABCDEA B C D E is a cyclic convex pentagon, and AC=BD=CE.ACA C=B D=C E . A C and BDB D intersect at XX, and BDB D and CEC E intersect at YY. If AX=6,XY=4A X=6, X Y=4, and YE=7Y E=7, then the area of pentagon ABCDEA B C D E can be written as abc\frac{a \sqrt{b}}{c}, where a,b,ca, b, c are integers, cc is positive, bb is square-free, and gcd(a,c)=1\operatorname{gcd}(a, c)=1. Find 100a+10b+c100 a+10 b+c.
Plain-text mathematical notation (without MathML)
ABCDE is a cyclic convex pentagon, and AC=BD=CE.AC and BD intersect at X, and BD and CE intersect at Y. If AX=6,XY=4, and YE=7, then the area of pentagon ABCDE can be written as (a√(b))/(c), where a,b,c are integers, c is positive, b is square-free, and gcd(a,c)=1. Find 100a+10b+c.
Original LaTeX notation
$A B C D E$ is a cyclic convex pentagon, and $A C=B D=C E . A C$ and $B D$ intersect at $X$, and $B D$ and $C E$ intersect at $Y$. If $A X=6, X Y=4$, and $Y E=7$, then the area of pentagon $A B C D E$ can be written as $\frac{a \sqrt{b}}{c}$, where $a, b, c$ are integers, $c$ is positive, $b$ is square-free, and $\operatorname{gcd}(a, c)=1$. Find $100 a+10 b+c$.

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task_id
4042c85b-36b5-506c-9c21-02c4779ab0b9
task_key
test--4042c85b-36b5-506c-9c21-02c4779ab0b9
task_revision_id
1
config / split
/ test

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