<Tri-2026-2299 >,hint

Line BP cut AC at B' and line MP cut AB at M'.

Then APB and APB' are congruent  and BP=PB'

since  M is the midpoint of BC, line MP//AC and cut AB at midpoint M'

By Ceva's theorem (AM'/M'B)x(BD/DM)x(MQ/QA)=1

Since AM'=M'B, BD/DM=AQ/QM, Hence DQ//AB.