<Qua-2025-773>, hint

Let v(AB)= v(DC)=v(a),  v(BC)=v(AD)=v(b)

AM/MB=m/1-m, BN/NC=n/1-n, DP/PC=p/1-p, DQ/QA=q/1-q

v(MN)=(1-m)v(a)+nv(b), v(QP)=pv(a)+qv(b) thus 1-m+p=1, n=q >>p=m. q=n

v(MA)=(1-m)v(a)=v(DP)=mv(a), 1-m=m. m=1/2

when M,N,P,Q are midpoints of AB,BC,CD,DA