Given circles $$ D $$ and $$ E $$, with $$ \overleftrightarrow{G J I} $$ tangent to $$ D $$ at point $$ G $$ and to $$ E $$ at point $$ I $$ and $$ \overleftarrow{F J H} $$ tangent to $$ D $$ at point $$ F $$ and to $$ E $$ at point $$ H $$. Identify a segment that is congruent to $$ \overline{F J} $$.

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1. From circle $$D$$, we know that if two tangent segments are drawn from the same external point, then the segments are congruent.
2. Here, point $$J$$ is external to circle $$D$$, and the segments $$\overline{FJ}$$ and $$\overline{GJ}$$ are tangent to the circle at points $$F$$ and $$G$$, respectively.
3. Therefore, by the tangent segment congruence theorem, we have
   $$
   \overline{FJ} \cong \overline{GJ}.
   $$
4. Thus, the segment that is congruent to $$\overline{FJ}$$ is $$\overline{GJ}$$.
The segment congruent to $$\overline{FJ}$$ is $$\overline{GJ}$$.

Given circles and , with tangent to at point and to at point and
tangent to at point and to at point . Identify a segment that is congruent
to .

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Given circles and , with tangent to at point and to at point and tangent to at point and to at point . Identify a segment that is congruent to .