Hi
SOCK is a parrallelogram .through a variable point H of[SC] draw the parallel to [OS]which cuts [SK]in E and [OC] in F. the parallel to [OC]cuts [OS]in M and [KC]in N.
Find the locus of I midpoint of [HM].
I assume that H is the intersection of EF and MN
It looks to me like the midpoint of HM could be anywhere in the left half of the parallelogram, like if P is the midpoint of OC and Q is the midpoint of SK then anywhere in SOPQ