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Omni-MATH / Regular hexagon ABCDEF has side length 2. A laser beam is fired inside the hexagon from point A and hits (BC)¯ at point G. The laser then reflects off (BC)¯ and hits the midpoint o…

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problem

Regular hexagon ABCDEFA B C D E F has side length 2. A laser beam is fired inside the hexagon from point AA and hits BC¯\overline{B C} at point GG. The laser then reflects off BC¯\overline{B C} and hits the midpoint of DE¯\overline{D E}. Find BGB G.
Plain-text mathematical notation (without MathML)
Regular hexagon ABCDEF has side length 2. A laser beam is fired inside the hexagon from point A and hits (BC)¯ at point G. The laser then reflects off (BC)¯ and hits the midpoint of (DE)¯. Find BG.
Original LaTeX notation
Regular hexagon $A B C D E F$ has side length 2. A laser beam is fired inside the hexagon from point $A$ and hits $\overline{B C}$ at point $G$. The laser then reflects off $\overline{B C}$ and hits the midpoint of $\overline{D E}$. Find $B G$.

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