The winners of the Motherwell v St Mirren replay will be playing at 7.20pm on the Saturday...
Scottish Cup: BBC to show Hibs v Inverness and all-Premiership tie in last eight
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From the sectionScottish Cup
Goals: BSC Glasgow 1-4 Hibernian
BBC Scotland will show live television coverage of Hibernian v Inverness CT and St Mirren or Motherwell v Aberdeen or Kilmarnock in the Scottish Cup.
Championship Inverness travel to take on top-flight Hibs in the last eight on Friday, 28 February at 19:45 GMT.
The replay between Motherwell and St Mirren takes place on Tuesday, with Kilmarnock and Aberdeen's replay the following night.
And the meeting of the winners will be on Saturday, 29 February at 19:20.
There will also BBC Radio Scotland coverage of Hearts v Rangers at 17:30 and holders Celtic's tie away St Johnstone at 15:00 on Sunday, 1 March.
Hibs, who beat Inverness at the quarter-final stage en route to winning the tournament in 2016, defeated BSC Glasgow in the fifth round while Caley Thistle shocked Premiership Livingston.
St Mirren drew 1-1 with Motherwell and Aberdeen were held to a 0-0 draw against Kilmarnock on Saturday.
Inverness CT win at Celtic 20 years ago is 'a JFK moment for Invernesians'
Scottish Cup quarter-finals
Friday, 28 February
Hibernian v Inverness CT (19:45) - live on BBC Scotland
Saturday, 29 February
Hearts v Rangers (17:30)
St Mirren/Motherwell v Aberdeen/Kilmarnock (19:20) - live on BBC Scotland
Sunday, 1 March
St Johnstone v Celtic (15:00)