Find the length of $LC$

Question

Given a quadrilateral $ABCD$ has a parallelogram $MLNK$ inscribed inside with $M,L,N,K$ lie on $AB,BC,CD,AD$ respectively with $AK=8,KD=10,BL=11$ and $AM=MB,CN=ND$. Find $LC$

Could someone one help me with this problem? I have asked before but I dun get any answer, sorry for asking again. I get this problem from Here

Answer 1

Let $P$ and $Q$ the midpoint of $AD$ and $BC$, respectively. quadrilateral $MPNQ$ is a parallelogram. triangle $KMP$ and triangle $LNQ$ are congruent triangles. Hence, $QL=KP=1$ and $BQ=CQ=10$ and $CL=9$. Here is the construction which have created using GeoGebra:

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