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In the figure, let
a = B R ⋅ T P ⋅ S Q P S ⋅ Q B ⋅ R T , b = W Z ⋅ V X ⋅ C Y Z V ⋅ Y W ⋅ X C .
What is the value of a − b ?
The answer is 0.
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2 solutions
We can use Menelaus theorem.
a = S Q P S ∗ B R Q B ∗ T P R T = − 1
b = V X Z V ∗ C Y X C ∗ W Z Y W = − 1
Thus
a − b = ( − 1 + 1 ) = 0
shouldn't a = 1 and b =1 ?
More simply, a and b are equal. Just check each element: PS corresponds to ZV, QB to XC, RT to YW etc. Therefore a=b and a-b=0.