Question Use Cevas Theorem to prove that the external bisect

Question Use Ceva\'s Theorem to prove that the external bisectors of two a iuternal bisector of the third angle are concurrent. SoLuTION: In the figure below, let t1, t2 and ls be the angle bisectors at A, B, sides at D. E. and F, respectively. The cevian product for the three cevians t, t, and (s is BD CE IF inc,. the points D and F divide the sides BC and AB externally, while the p nternally

Solution

I sense an error here

BD/DC is to be taken negative because D divides the segment externally and D does not lie between B and C.

That\'s why AF/FB is also taken negative.

Whereas , CE/EA will be taken as positive as Well divides the segment internally and lies in between C and A.

You also check the ceva\'s theorem official proof for the authencity of this convention.

Thanks.