Holders Dundee United have been handed a home tie against Motherwell in the last eight of the Scottish Cup.
Inverness will host either Rangers or Celtic, once their replay has been decided in early March.
Aberdeen's reward for a late victory over Dunfermline is an away tie against St Mirren.
And Brechin City, in the quarter-finals for the first time in their history, face the winner between St Johnstone or Partick Thistle.
Ties are scheduled to be played on 12 and 13 March.
Scottish Cup quarter-final draw: Brechin v St Johnstone or Partick Thistle
Dundee United v Motherwell
Inverness v Rangers or Celtic
St Mirren v Aberdeen
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