In triangle
A
B
C
above, if
A
E
=
E
C
and
A
D
=
D
G
=
G
B
, find
F
G
C
F
. If you've come to the conclusion that the value cannot be derived, type in 0.
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Thanx d bro.
How did you derive BG to -1 ?
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BG and AB are in opposite direction, so they must be of different sign.
Using a point mass system: M A = M C = 1 so M E = M A + M C = 2 Now A G : G B = M B : M A = 2 : 1 ∴ M A = 2 M G = M A + M B = 3 ∴ F G C F = M C M G = 3
What is point mass?
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You imagine that you have a mass at a point and that you want the weights to balance on the lines, in the same way that weights balance on levers. If you're still not sure, see the Barycentric Coordinates Wiki on Brilliant
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Apply Menelaus' theorem
E A C E ⋅ B G A B ⋅ F C G F = − 1
1 1 ⋅ − 1 3 ⋅ F C G F = − 1
F G C F = 3