+380 In parallelogram EFGH, let M be the point on \overline{EF} such that FM:ME = 1:1, and let N be the point on \overline{EH} such that HN:NE = 1:1. Line segments \overline{FH} and \overline{GM} intersect at P, and line segments \overline{FH} and GN intersect at Q. Find PQ/FH.
+130081 
Triangle HQN sinilar to triangle FQG Triangle MPF similar to triangle GPH
HQ/HN = FQ/FG MF/PF = GH/PH
HQ/2 = FQ/4 2/PF = 4/PH
HQ/FQ = 2/4 = 1/2 PF/PH = 2/4 = 1/2
HQ = ( 1/3)FH
PF = (1/3)FH
FH - HQ - PF = PQ
FH - (1/3)FH - (1/3)FH = (1/3)FH = PQ
PQ / FH = (1/3)FH / FH = 1/3
