Consider an triangle ABC with M as the middle point of the side AB.
On the straight line through AB you put the angle ∠ ACM at A and the angle ∠ MCB at B. Now you have two new lines. The new lines should be on the same side of AB as C.
Proof that the intersection point of the two new lines is located on the line through CM.
The Attempt at a Solution
I wanted to use Ceva`s Theorem but I could not use it :(
I hope you can give me some advice.