+1036 In parallelogram EFGH, let M be the point on EF such that FM:ME = 3:5 and let N be the point on EH such that HN:NE = 2:5. Line segments FH and GM intersect at P, and line segments FH and GN intersect at Q. Find PQ/FH.
+128578 PQ / FH 
Triangle HQN similar to triangle FQG Triangle MPF similar to triangle GPH
HQ / HN = FQ / FG MF / PF = GH / PH
HQ / 2 = FQ / 7 3 / PF = 8 / PH
HQ/FQ = 2/7 PF / PH= 3/8
HQ = (2/9)FH
PF = ( 3/11)FH
HQ = (22/99)FH
FP = (37/99)FH
PQ = [ 99 - 22 - 27 ] / 99 = 50/99 FH
PQ / FH = 50 / 99
