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Sagot :
In the given triangle FCE and GCD
angle C is common
as line GD || FE
angle EFC = angle DGC (corresponding angle)
Similarly
Angle CDG = AngleCEF (Corresponding angle)
By Angle Angle similarity, triangle FCE and GCD are similar
From thr properties of similar triangle,
The ratio of corresponding sides of similar triangle are equal
[tex]\begin{gathered} In\text{ }\Delta FCE\text{ \&}\Delta\text{ GCD} \\ \frac{FC}{GC}=\frac{CE}{CD}=\frac{EF}{DG} \end{gathered}[/tex]substitute the value: GC = 10, CD = 12, DE = 72
as: CE = CD + DE
CE = 12 + 72
CE = 84
[tex]\begin{gathered} \frac{FC}{GC}=\frac{CE}{CD}=\frac{EF}{DG} \\ \frac{FC}{10}=\frac{84}{12}=\frac{EF}{DG} \end{gathered}[/tex]For the length CF, simplify first two expression:
[tex]\begin{gathered} \frac{CF}{10}=\frac{84}{12} \\ CF=\frac{84\times10}{12} \\ CF=7\times10 \\ CF=70 \end{gathered}[/tex]Answer : CF = 70
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