The analogy of projective theorem in geometry, the topic is the eighth question, how to prove it, thank you.

If you want to prove AB? =BD×BC, only need to prove AB/BD=BC/AB, which is easy to prove by using the similarity and equivalence ratio of right triangle.

If we want to prove the equation of area, the idea of solving the problem has been explained, because the base BC of △ BOC and △ BCD is the same, and the heights are OE and DE respectively, while in △ABC, AE is high, and in △AED, AE? =ED×EO, so the area equation is easy to prove.