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Omni-MATH / Let △ABC be a triangle with AB=7,BC=1, and CA=4√(3). The angle trisectors of C intersect (AB)¯ at D and E, and lines (AC)¯ and (BC)¯ intersect the circumcircle of △CDE again at X a…

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problem

Let △ABC\triangle A B C be a triangle with AB=7,BC=1A B=7, B C=1, and CA=43C A=4 \sqrt{3}. The angle trisectors of CC intersect AB¯\overline{A B} at DD and EE, and lines AC¯\overline{A C} and BC¯\overline{B C} intersect the circumcircle of △CDE\triangle C D E again at XX and YY, respectively. Find the length of XYX Y.
Plain-text mathematical notation (without MathML)
Let △ABC be a triangle with AB=7,BC=1, and CA=4√(3). The angle trisectors of C intersect (AB)¯ at D and E, and lines (AC)¯ and (BC)¯ intersect the circumcircle of △CDE again at X and Y, respectively. Find the length of XY.
Original LaTeX notation
Let $\triangle A B C$ be a triangle with $A B=7, B C=1$, and $C A=4 \sqrt{3}$. The angle trisectors of $C$ intersect $\overline{A B}$ at $D$ and $E$, and lines $\overline{A C}$ and $\overline{B C}$ intersect the circumcircle of $\triangle C D E$ again at $X$ and $Y$, respectively. Find the length of $X Y$.

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Source and history

task_id
45225eca-2dab-5ce4-a6e6-e95374fbc174
task_key
test--45225eca-2dab-5ce4-a6e6-e95374fbc174
task_revision_id
1
config / split
/ test

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