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