In an equilateral triangle ${ABC}$ the segments ${ED}$ and ${GF}$ are drawn to obtain two equilateral triangles ${ADE}$ and ${GFC}$ with sides 1 and 100 (points $E$ and $G$ are on the side ${AC}$ ). The segments ${EF}$ and ${DG}$ meet at point $O$ so that the angle ${EOG}$ is equal to ${120}^{ \circ }$ . What is the length of the side of the triangle ${ABC}$ ? Mikhail Evdokimov
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