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'
- 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 ...
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