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    Proofs : Collinear and Distinct; Boomerang Quadrilateral

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    1- Prove that if AF/FB = AF'/F'B where A, B, F, F' are collinear and distinct then F does not have to equal F'

    2- Suppose that the sides AB, BC, CD and DA of a quadrilateral ABCD are cut by a line at the points A' B' C' D' respectively, show that AA'/A'B * BB'/B'C * CC'/C'D * DD'/D'A = +1

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    Solution Preview

    Question 1
    - prove that if AF/FB = AF'/F'B where A, B, F, F' are collinear and distinct then F does not have to equal F'
    Solution to Q1:
    ============
    We need only produce one example where the conditions hold and where F is not F'
    Place your points on the x-axis, <----A----F----B----F'----> and give them coordinates, say
    A(0,0) F(f,0) B(b,0) F'(f',0) so 0 < f < b < f'
    [I used this order after trial and error showed it would work better.]
    Then AF/FB = f/(b-f) and AF'/F'B = f'/(f'-b)
    Equating them to give us a condition which must ...

    Solution Summary

    Geometry proofs are provided. The solution is detailed and well presented. A diagram is included

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