2 column geometry proof?

Question

Given: triangle PQR aith altitude QA, angle bisector QB, and median QM, with B between A and M.

Prove: QA < QB< QM
(triangle drawn is an acute triangle) sorry I cant draw the picture

Q on top
P A B M R across the bottom (longest end on the right)
SHOULD BE 10 STEPS AND I AM SO LOST

Answer 1

It is clear that QA QB M is closer from QR because the triangles QPM and QRM have same area. since A is closer from QP that implies that B is between A and M so AB