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Scottish Cup holders Celtic will face either Aberdeen or Rangers in the semi-finals of this year's tournament.
Neil Lennon's men defeated Hibernian on Saturday while Steven Gerrard's Rangers drew at Pittodrie.
Inverness Caledonian Thistle were rewarded for their last-gasp 2-1 victory over Dundee United with a tie against either Partick Thistle or Hearts, who drew 1-1 at Firhill on Monday night.
The ties will be played on 13/14 April.
Celtic won the trophy in the past two years to complete a double Treble under Brendan Rodgers.
Rodgers also led Celtic to this season's League Cup before departing for Leicester City and Lennon has maintained the side's eight-point lead at the top of the Premiership.
Rangers host Aberdeen and Hearts welcome Thistle in next Tuesday's quarter-final replays.
Partick Thistle/Hearts v Inverness CT
Aberdeen/Rangers v Celtic
