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GeoGebraΤάξη GeoGebra

Demonstration of Ceva's Theorem and its Converse

In the construction below, points D, E, and F can be moved.
  • Can you make the product of the ratios be equal to 1 without having the segments AD, BF, and CE be concurrent?
  • Can you make the segments AD, BF, and CE be concurrent without the product of the ratios being equal to 1?
How does Theorem 4.13 answer the above questions?