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Omni-MATH / Squares ABCD and DEFG have side lengths 1 and (1)/(3), respectively, where E is on (CD)¯ and points A,D,G lie on a line in that order. Line CF meets line AG at X. The length AX can…

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problem

Squares ABCDA B C D and DEFGD E F G have side lengths 1 and 13\frac{1}{3}, respectively, where EE is on CD¯\overline{C D} and points A,D,GA, D, G lie on a line in that order. Line CFC F meets line AGA G at XX. The length AXA X can be written as mn\frac{m}{n}, where m,nm, n are positive integers and gcd(m,n)=1\operatorname{gcd}(m, n)=1. Find 100m+n100 m+n.
Plain-text mathematical notation (without MathML)
Squares ABCD and DEFG have side lengths 1 and (1)/(3), respectively, where E is on (CD)¯ and points A,D,G lie on a line in that order. Line CF meets line AG at X. The length AX can be written as (m)/(n), where m,n are positive integers and gcd(m,n)=1. Find 100m+n.
Original LaTeX notation
Squares $A B C D$ and $D E F G$ have side lengths 1 and $\frac{1}{3}$, respectively, where $E$ is on $\overline{C D}$ and points $A, D, G$ lie on a line in that order. Line $C F$ meets line $A G$ at $X$. The length $A X$ can be written as $\frac{m}{n}$, where $m, n$ are positive integers and $\operatorname{gcd}(m, n)=1$. Find $100 m+n$.

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Source and history

task_id
e6dc599d-b2f2-5529-b1a7-e59d1cf82e75
task_key
test--e6dc599d-b2f2-5529-b1a7-e59d1cf82e75
task_revision_id
1
config / split
/ test

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