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Omni-MATH / Let ABCD be a square of side length 5. A circle passing through A is tangent to segment CD at T and meets AB and AD again at X≠A and Y≠A, respectively. Given that XY=6, compute AT.

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problem

Let ABCDA B C D be a square of side length 5. A circle passing through AA is tangent to segment CDC D at TT and meets ABA B and ADA D again at X≠AX \neq A and Y≠AY \neq A, respectively. Given that XY=6X Y=6, compute ATA T.
Plain-text mathematical notation (without MathML)
Let ABCD be a square of side length 5. A circle passing through A is tangent to segment CD at T and meets AB and AD again at X≠A and Y≠A, respectively. Given that XY=6, compute AT.
Original LaTeX notation
Let $A B C D$ be a square of side length 5. A circle passing through $A$ is tangent to segment $C D$ at $T$ and meets $A B$ and $A D$ again at $X \neq A$ and $Y \neq A$, respectively. Given that $X Y=6$, compute $A T$.

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Source and history

task_id
c06d7dc4-4107-5185-8507-15c4ced7ce3b
task_key
test--c06d7dc4-4107-5185-8507-15c4ced7ce3b
task_revision_id
1
config / split
/ test

Official source

initial import