Euclidean geometry problems - mostly Menelaus' theorem

3. The incircle of touches the sides at the points respectively, and is produced to meet at

Show that

4.A circle meets side of at points and , at and , and at and . Show that if are concurrent, then are also concurrent.

6.In , let and be points on the sides and , respectively, with . If

the median intersects the segment at the point , show that

I'm pretty sure they all just require creative use of Menelaus' theorem, but I can't seem to figure out in which ways :(

I don't want the questions solved entirely for me, maybe just some hints (or rot13 the answer so I am encouraged to do it myself before checking)

Turns out I had to use power of a point as well, done now