Question
In triangle DEF, point G lies on EF such that ∠DGE =
∠DGF. If DE = 40 cm, DF = 20 cm, and EF = 24 cm, find the length of EG.Solution
ATQ,
Since ∠DGE = ∠DGF, DG is the angle bisector of ∠D.
By Angle Bisector Theorem:
DE / DF = EG / GF
Let EG = x cm
Then GF = 24 - x cm
40 / 20 = x / (24 - x)
⇒ 2 / 1 = x / (24 - x)
2(24 - x) = x
48 - 2x = x
48 = 3x
x = 16
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