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I’ll leave you with Ewan Murray’s report from Hampden Park:

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Callum McGregor says he is “really proud of the players, it’s been a difficult week, a big change … The whole place comes alive again, you can see how much it means to the players.”

On his goal, he says: “If you don’t shoot you don’t score, it was a big moment in the game.”

Callum Osmand says it’s “the best day of my life” as he celebrates his first Celtic goal on just his second appearance. He recalls being out of the squad and “running in the rain up and down the pitch”, saying that it has prepared him as a player.

On Danny Röhl’s impact, Osmand says: “He thinks very highly of me and that gives you the boost you need. He’s given me the confidence and trust. That’s all you need form a manager. Hopefully this is just the start.”

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Celtic will face St Mirren in the final at Hampden Park on Sunday 14 December.

ShareFull-time: Celtic 3-1 Rangers (aet)

Celtic are through to the League Cup final but boy did they have to work hard! Rangers were already trailing to Johnny Kenny’s opener when Thelo Aasgaard was shown a straight red for a challenge on Anthony Ralston.

Danny Röhl didn’t compromise and his team fought on, forcing a penalty with 10 minutes to go when Ralston was penalised for handball. James Tavernier sent the tie to extra time but Celtic made the most of their man advantage.

Callum McGregor’s thunderous strike saw them regain the lead and substitute Callum Osmand finally got the goal his performance deserved when he converted Kieran Tierney’s cross to put the tie beyond doubt.

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Updated at 11.38 EST

120+1 min: The olés are out for Celtic. Balikwisha wins a corner after his cross is diverted behind.

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120 min: Two minutes added.

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119 min: The Rangers half of Hampden has emptied out. Nobody has left the other half.

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Updated at 11.32 EST

118 min: Balikwisha finds Tierney, whose shot is blocked to cries of handball. Celtic are taking plenty of time over restarting the game.

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117 min: Forrest almost picks out Balikwisha in a dangerous position. Gassama is now being booed with every touch.

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116 min: Trusty soldiers on. Rangers try to give the ball back to Schmeichel after Celtic kicked it out but Gassama is having none of it. He chases it down but is stopped in his tracks. Ralston, understandably, takes issue with this. That would have been controversial.

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114 min: Trusty has a convenient touch of cramp and needs his leg stretching. The game looks up for Rangers now.

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113 min: Osmand is causing all sorts of trouble for Rangers. Forrest is penalised for what looked like a great challenge on Moore – O’Neill goes mad on the touchline. Just like old times.

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111 min: O’Neill sends on Balikwisha for Maeda. Celtic have a proper cushion now.

ShareGOAL! Celtic 3-1 Rangers (Osmand 109)

Callum Osmand’s first goal for Celtic surely sends them into the final! Tierney whips a cross into the corridor of uncertainty and the 19-year-old former Fulham youngster flings himself at it and diverts it into an empty net. He kisses the badge in the celebration. A dream moment!

Celtic’s Callum Osmand celebrates scoring their third goal. Photograph: Russell Cheyne/ReutersShare

Updated at 11.32 EST

107 min: Osmand drives at the Rangers backline and forces Tavernier into a foul. McGregor spots Hatate in behind from the free-kick but the flag is up.

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Back under way. We’ve swapped ends.

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Updated at 11.18 EST

Zach Neeley writes in:

To immediately go down a goal and now need to chase for 30 minutes after all the effort to make it to extra time. My legs would rebel.

Even if they come away beaten, Danny Röhl and Rangers will earn tremendous credit for their attitude in this game.

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Half-time in extra time: Celtic are 15 minutes from the League Cup final.

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105+1 min: Tierney launches a throw into the box and Hatate is bundled over by Moore. The referee waves away appeals for a penalty.

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105 min: One minute added.

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104 min: Osmand goes close again! Forrest gets to the byline, cuts it back for the striker, who turns and strikes low but Butland’s legs get in the way. Souttar goes into the book for pulling back Osmand on halfway.

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102 min: Schmeichel makes himself big again as Miovski tries to get on the end of a loose ball in the penalty area. The Celtic keeper sticks his glove out to divert it out of harm’s way. Joe Rothwell is on for Djiga.

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100 min: It’s Schmeichel’s turn to make a crucial stop! Miovski plays Gassama in but the Dane is quick off his line again and spreads himself in trademark fashion.

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Updated at 11.09 EST

98 min: Osmand has another chance from the corner but can’t guide an awkward header on target.

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97 min: What a save from Butland! At full stretch he gets fingertips on the ball as Osmand looks to guide a header towards the bottom corner.

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96 min: Celtic look in control now, keeping possession in their own half. Rangers are still pressing, to be fair.

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Butland might be disappointed with that. It wasn’t in the corner – he may claim he was unsighted.

ShareGOAL! Celtic 2-1 Rangers (McGregor 93)

A captain’s goal! McGregor receives it on the edge of the box, takes one touch to get it out of his feet and launches a left-footed drive that flies past Butland and high into the net! Celtic hit the front.

Celtic’s Callum McGregor scores their side’s second goal. Photograph: Andrew Milligan/PAShare

Updated at 11.34 EST

92 min: Rangers are going to need all the help they can get. Röhl seems to have got their approach spot on since going down to 10 men.

ShareExtra time begins

Rangers have sent for Antman. He’s on for Raskin.

ShareFull-time: Celtic 1-1 Rangers

We’re heading to extra time! Tierney has the last chance of regulation time but his right-footed shot is deflected wide and the referee blows his whistle. Such a valiant effort from Rangers, a man down that whole half.

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90+4 min: Röhl tries to take the sting out of it with Max Aarons replacing Meghoma. Celtic go forward one last time …

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90+2 min: Hatate blazes over! Forrest is involved again as he knocks a ball back into a central position and the Japan midfielder strides on to it but sends it over the bar.

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90+1 min: Nobody can get a touch on Tierney’s inviting cross and Rangers clear. It’s all hands on deck for the 10 men now.

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90 min: Engels’ corner produces pinball and the Celtic fans cry out for handball but VAR says no. Four minutes to be added.

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89 min: Forrest is having a real impact. His cross is headed behind for a corner …

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88 min: Forrest sends Osmand through again. The teenager gets past Souttar before Meghoma comes in and bumps him over. No foul given.

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87 min: The momentum is with Celtic once again. Engels swings in a couple of corners but they are not of the quality of his first-half deliveries.

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85 min: Crucial save from Butland! Forrest plays Osmand in on the left but the 19-year-old can’t squeeze the ball under Butland. Huge chance!

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84 min: Tavernier’s corner is headed clear. Celtic pile forward but Ralston’s long ball is dealt with by Djiga.

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83 min: Rangers are emboldened. Meghoma pings the ball off Ralston and it goes out for a corner …

ShareGOAL! Celtic 1-1 Rangers (Tavernier 81pen)

Tavernier levels it! He whips his penalty across his body and into the bottom corner. Schmeichel dives the right way but can’t get near it.

Rangers’ James Tavernier celebrates scoring their first goal with Mikey Moore. Photograph: Lee Smith/Action Images/ReutersShare

Updated at 10.45 EST

80 min: Penalty to Rangers! Gassama takes aim and Ralston flings himself at the shot John-Terry-style. The referee hesitates before pointing to the spot for handball. His arms are by his side but the penalty stands. Ralston escapes a second yellow. It’s Tavernier against Schmeichel from the spot …

The ball hits Anthony Ralston of Celtic on the arms. Photograph: Stuart Wallace/ShutterstockShare

Updated at 10.51 EST

78 min: Saracchi’s work is done. Kieran Tierney heads on to help Celtic defend the Rangers corner. Tavernier’s cross goes all the way through.

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76 min: Big chance for Rangers! Moore sends a ball in behind for Gassama to chase. The winger takes it under control but just as he’s about to pull the trigger, Scales slides in. Vital defending.

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74 min: Forrest pulls the ball back for Hatate, whose shot is fumbled by Butland but eventually gathered.

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72 min: Nygren and Kenny are replaced by Reo Hatate and Callum Osmand for Celtic. The latter is making just his second appearance for the club. Rangers send on Mikey Moore and Bojan Miovski for Chermiti and Diomande.

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