(D) $\triangle ADP \sim \triangle CBP$
When two chords AB and CD intersect at P inside a circle, ∠DAP = ∠BCP (angles in the same segment) and ∠APD = ∠CPB (vertically opposite angles), so △ADP ~ △CBP by AA similarity.
The key is matching vertices correctly: ∠A = ∠C (same segment arc BD/CD) and ∠D = ∠B (same segment), with vertically opposite angles at P. Students often make errors in vertex correspondence — always verify that corresponding angles match before writing the similarity statement.