<Solid-2025-262>, hint

By coordinate system let A(0,0,0), B(1,0,0), C(1,1,0), A'(0,0,1)

Foot of perpendicular from A to plane A'CD is the midpoint of A'D, M(0,1/2,1/2)

Foot of perpendicular  from B to A'C be N, then A'N:NC=2:1 , because

triangle A'BC is right, <A'BC=90, A'B^2=A'Nx A'C, BC^2=CN x CA'. Hence N(2/3, 2/3, 1/3)

Since P(2,1,0).You can prove by equation of line MP, N is on line MP.