<Qua-2025-777>, hint

Consider coordinate, let B(0,0), A(0,1), C(1,o), D(1,1) and O be the intersection of AC and BD. Let E on OD such that ED/EB=t/(1-t).

Since AH ㅗ BE, EHㅗAB  H(t,1-t).

EKㅗAD  AKㅗBD, K(1-t,t). Hece BH=(t, 1-t), KD={1-(1-t), !-t} =(t, 1-t)