Given a triangle ABC, Let A',B',C' be midpoints of [BC],[CA] and [AB], respectively:
a) Consider L element of BC-{B,C}, M element of CA-{C,A}, N element of AB-{A,B} such that AL,BM,CN are concurrent if P,Q,R are respective midpoints of [AL], [BM],[Cn] prove that
PA',QB',RC' are concurrent or parallel
b) Consider collinear points
U element of BC-{B,C}
V element of CA-{C,A}
W element of AB-{A,B}
Prove that respectively midpoints X,Y,Z of [AU],[BV],[CW] are collinear