∴∠DAQ+∠DQA=90,∠CDP+∠CPD=90,∠DQA+∠CDP=90
∴∠DAQ=∠CDP
∫AD = DC,∠ADQ=∠DCP=90
∴△ADQ≌△DCP
∴DQ=CP
ABCD is a square
∴OD=OC,∠ODQ=∠OCP=45
∴△DOQ≌△COP
∴∠DOQ=∠COP
∴∠DOQ+∠QOC=∠QOC+∠COP=90
∴OQ⊥OP