Ceva's theorem, as described in wiki
Given a triangle ABC, let the lines AO, BO and CO be drawn from the vertices to a common point O (not on one of the sides of ABC), to meet opposite sides at D, E and F respectively. (The segments AD, BE, and CF are known as cevians.) Then, using signed lengths of segments,
$$\frac {AF}{FB}\cdot \frac {BD}{DC}\cdot \frac {CE}{EA}=1.$$
, is about the lengths of the triangle's sides split by a commont point.
I wonder, if it can be extended to angles? -- if we name angle OAB as $\alpha_1$, OAC as $\alpha_2$, OBC as $\beta_1$, OBA as $\beta_2$, OCA as $\gamma_1$ and OCB as $\gamma_2$, is there a conclusion of the relationship among them?
