Question

Prove that if AL, BM, and CN, are proper Cevian lines that are concurrent at an ordinary point P, then either all three of the points L, M, and N, lie on triangle ABC or exactly one of them does. Hint: The three sidelines divide the exterior of triangle ABC into six regions. consider the possibility that P lies in each of them separately. Don't forget that one or more of the points L, M, and N, might be ideal.

Answer 1

i am sending you answer where these are showing how these lines are concurrent at p also if they are concurrent then point must lie on triangle. I try to help out via ceva's theorem check it out.