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Omni-MATH / Circle O has chord AB. A circle is tangent to O at T and tangent to AB at X such that AX=2XB. What is …

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problem

Circle OO has chord ABA B. A circle is tangent to OO at TT and tangent to ABA B at XX such that AX=2XBA X=2 X B. What is \frac{A T}{B T}?
Plain-text mathematical notation (without MathML)
Circle O has chord AB. A circle is tangent to O at T and tangent to AB at X such that AX=2XB. What is \frac{A T}{B T}?
Original LaTeX notation
Circle $O$ has chord $A B$. A circle is tangent to $O$ at $T$ and tangent to $A B$ at $X$ such that $A X=2 X B$. What is \frac{A T}{B T}?

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