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A reminder of where we stand with the Scottish Cup: Celtic join Dunfermline and Falkirk in the hat (is it still a hat? probably not). The last quarter-final is St Mirren v Partick Thistle this evening, after which we get the semi-final draw.

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Gerard Brett, a relieved Celtic supporter, emails: “I reckon Martin O’Neill played for penalties. Shame about the brouhaha at the end about which Danny Röhl is disingenuously claiming to be unaware.

“As a Celtic fan I can say we are awful, a real hotchpotch. But Rangers are shocking. They should have dispatched us today. MON is the crucial ingredient. God bless his cotton socks!”

I agree both sides are clearly not firing on all cylinders right now, but it’s making for an intriguing season in Scotland if nothing else.

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“I was in the tunnel at the end, I didn’t see something,” says Danny Röhl, taking the patented A Wenger approach when asked about the supporters on the pitch. To be fair to him, I can well imagine he headed for the dressing room pretty quickly after the spot-kicks.

Of the game the Rangers manager says: “The result is disappointing … We were the better team over 120 minutes: 24-one in shots, but football is about results – and we didn’t take the result we deserved today. We are disappointed. But next week we go again: it’s nine finals to go.”

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As for Danny Röhl, the Rangers manager has now seen his side suffer Old Firm agony twice in two weekends, despite not losing a game in normal (or extra) time.

Today Rangers had 24 attempts on goal over 120 minutes but only six on target and, obviously, zero goals. Celtic had no attempts on target but all four of their spot-kicks hit the mark.

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“The crowd kept us going,” says Martin O’Neill, as he adds that he hopes the post-shootout aggro on the pitch doesn’t mean the powers-that-be view away fans at Old Firm games as a negative. Something we can, possibly, all agree upon.

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Martin O’Neill speaks on TV. “It’s unfortunate,” he says of the fans on the pitch at the end, “but hopefully it doesn’t dilute the performance in terms of character – all the things that we had. It was our fourth game in 10 days but we defended absolutely magnificently. We got blocks on, boys throwing their bodies on the line – I’ve got the utmost regard for the team.

“Old Firm games – they’re explosive games, they always have been. And maybe that’s one of the reasons the derby is one of the best in the world.”

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“It’s a tough one – there’s no derby like it … listen, it’s not going to take away from what we’ve done here,” says Celtic’s keeper Viljami Sinisalo when asked about the scenes at the end. “We’ve come here and we’ve beaten them and we’re into the next round of the cup.”

Celtic’s final penalty hero, Tomas Cvancara, has blood splattered on his shirt as he stands alongside him talking to Premier Sports. Yikes. You assume that’s just from a hard-fought game rather than the player getting caught up in the pitch invasion, of course.

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Updated at 12.07 EDT

Maybe it’s just a trick of the mind but it does feel as though the side who have struggled in the 120 minutes have an edge in penalty shootouts. As if they have nothing to lose (though I’m not sure “nothing to lose” ever applies to an Old Firm encounter).

Celtic won the shootout decisively despite – I assume – losing both tosses, as they took second and in front of the Rangers fans.

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Updated at 11.59 EDT

Security are lined up in front of the Broomloan Stand at Ibrox but at least it’s quiet on the pitch now.

You get the feeling Celtic fans won’t be let out of it any time soon, but they’re probably enjoying themselves a fair bit.

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Worth saying it was four pretty flawless Celtic penalties in the shootout, after their side were under pressure for much of the 120 minutes (albeit Rangers struggled to create clear-cut changes).

For Rangers, Tavernier – so often the spot-kick hero – struck the bar, while Gassama cleared it. He looked devastated after his miss.

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Pretty ugly scenes at the end of play with both sets of players quickly escorted off the pitch. However it looks like the fans are racing now to get back to the stands, rather than to get to each other. Small mercies.

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Well, the high emotions have spread to the stands – several celebrating Celtic supporters raced on to the pitch after their side won the shootout 4-2. Rangers fans are now on the pitch in response, along with several flares.

The authorities are doing their best to keep the peace here.

Celtic fans celebrate on the pitch after the match. Photograph: Lee Smith/Action Images/ReutersShare

Updated at 11.59 EDT

Celtic win 4-2 on penalties against Rangers!

Tomas Cvancara rockets the ball into the net to seal the penalty shootout for Celtic!

Tomas Cvancara (left) celebrates with his team mates after scoring the winning penalty. Photograph: Steve Welsh/PAShare

Updated at 12.00 EDT

Penalties: Rangers 2-3 Celtic: Gassama misses!

Gassama puts it over the bar!

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Updated at 11.50 EDT

Penalties: Rangers 2-3 Celtic: Hatate scores!

Hatate hammers it home! Clean as a whistle.

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Penalties: Rangers 2-2 Celtic: Naderi scores!

Another close one! Naderi just slips it under the keeper’s outstretched hand.

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Penalties: Rangers 1-2 Celtic: Trusty scores!

Trusty calmly sidefoots it into the corner. Trusty by name.

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Penalties: Rangers 1-1 Celtic: Bajrami scores!

Oh that one just squeezes under Sinisalo and into the net. So close.

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Penalties: Rangers 0-1 Celtic: Oxlade-Chamberlain scores!

The Ox goes straight down the middle to give the visitors the early edge.

Alex Oxlade-Chamberlain scores. Photograph: Lee Smith/Action Images/ReutersShare

Updated at 11.45 EDT

Penalties: Rangers 0-0 Celtic: Tavernier misses!

James Tavernier cracks the ball on to the bar. Oh my what a start.

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Penalties will be in front of the Rangers fans, away from the away end. And it’s going to be Rangers to take first. Its Tavernier up first.

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So, which end are we going to be taking the penalties in front of? Who will go first?

The big questions. My (sketchy) research suggests there have been just two penalty shootouts between the sides over the years. One apiece.

ShareFull time! Rangers 0-0 Celtic

We are going to penalties.

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119 min: Important interception Souttar to stop a fine Celtic attack! That was some nice interplay.

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118 min: Tavernier’s pass, Bajrami can’t quite get on the end of it. A bit too much on it and Bajrami hops up and down on the spot. We are almost at the end.

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117 min: Rangers on the attack, Gassama crosses but it’s a Celtic head on the ball to put it clear.

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115 min: Will one side get a chance at a winner in the final five minutes? Araujo picks up a booking for a (tactical) foul to stop Rangers breaking.

Raskin has Araujo by the collar! But both men seem equal there in giving each other some verbals. Fair enough.

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Updated at 11.30 EDT

114 min: Chermiti is in space on the left and crosses the ball in, but Bernardo chests it calmly back to his goalkeeper.

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111 min: Celtic are almost let in! Souttar’s poor, short pass just gets to Butland, who was out rapidly enough to hammer it clear – good work from the Rangers keeper.

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Updated at 11.25 EDT

110 min: Now Bernardo picks up a yellow card for pulling back Raskin by the arm as he tries to break away. A clear one.

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108 min: Paulo Bernardo with some fleet feet inside the Rangers’ box! Souttar defended well to stop him wriggling into an opening, good play from two fresh players.

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107 min: Murray clears well for Celtic but it’s another wave of Rangers pressure. Another towering Murray header clears it.

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106 min: We’re back under way; Rangers’ John Souttar is on for Djiga. The hosts put the ball into the Celtic box but Oxlade-Chamberlain clears it.

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So it’s now 1-1 on goals that have been ruled out but it was clear quickly on replays that the ball had touched Emmanuel Fernandez on the arm before it was bundled into the net. A case of VAR clearing up an obvious one pretty quickly. (Cue a VARdisaster in the second half of extra time.)

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Peep-peep: it’s the break in added time. We have 15 minutes to go until penalties.

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105 min: Rangers have a corner on the verge of the half-time break in extra time. Murray heads it clear. Tavernier’s deliveries have been a threat since he came on.

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103 min: Chermiti with another chance after an inviting Tavernier cross – he puts it wide of the post! He really should be testing the goalkeeper there. Rangers on top at the moment, Celtic clinging on.

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99 min: Fernandez has the ball in the net from a corner – Ibrox goes wild! But it’s pretty clearly touched his arm before he bundled it into the net. VAR are going to overturn this … yes! It does not take long; that was fairly clear.

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Updated at 11.10 EDT

98 min: Chermiti is in behind the Celtic defence! He has a chance to shoot but it’s a take effort and it’s cleared. That was a chance.

Youssef Chermiti goes close for Rangers. Photograph: Steve Welsh/PAShare

Updated at 11.12 EDT

97 min: Tavernier with a dangerous ball into the box, Sinisalo springs into action to punch it clear.

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Updated at 11.10 EDT

95 min: Naderi wins the ball and tries to play it in but can’t find a gap in the Celtic defence. Oxlade-Chamberlain is pulled up for a challenge on Chermiti. It’s not the most free-flowing in extra time, let’s say.

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Updated at 11.10 EDT

93 min: Chermiti runs at the Celtic defence but when he has the chance to get a shot away, it’s blocked from close range.

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Updated at 11.10 EDT

Zach Neeley has a question re. the Rangers-Celtic shot chart (on which Rangers dominate the numbers, 19-1, but with precious few on target): “Currently posing the question to fans: is it better to have tried and failed or to have not tried at all?

ShareExtra time kicks off

Rangers get us started – and they have James Tavernier on in place of Sterling.

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Stat from normal time: Rangers had 19 attempts on goal but only four on target. A sign of the lack of clinical edge on show. Sinisalo has looked sharp with what he has had to do.

ShareFull time: Rangers 0-0 Celtic

We’re going to extra time at Ibrox.

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90+3 min: Celtic get it clear but the ball is soon back with Rangers. Time for one final chance? Raskin’s cross flies well out of play.

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90+2min: A Rangers corner. This could be the final chance of normal time.

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90+1min: Sinisalo launches the ball into a Rangers box, but the hosts win it back and break. Chermiti has the ball inside the Celtic box! But Murray puts in a superb and necessary block. Great play all round.

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89 min: Sterling rises to head Celtic’s corner clear. We’re going to get three additional minutes before extra time.

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87 min: Oxlade-Chamberlain plays a pass straight to Fernandez; Rommens pulls down Forrest. It’s scrappy. But will we see a late goal? Celtic have a corner.

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86 min: Fernandez shuts down a Celtic attack, the ball goes down the other end but Sinisalo is out quickly once more to claim it.

Emmanuel Fernandez clears the danger from Yang Hyun-Jun. Photograph: Andrew Milligan/PAShare

Updated at 10.54 EDT

85 min: Rommens takes a corner for Rangers, Raskin with a great header! But Nygren does really well to hook it clear.

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83 min: Celtic play a through ball but any opening is snuffed out by Raskin. Hatate is booked after he fouls Naderi having been dispossessed himself. Some tired play out there.

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82 min: Rangers have possession but their passing looks a little tired and Chermiti is caught offside. Celtic’s chance to build something – Sterling fouls Mvuka. He has to be careful, being on a booking.

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80 min: Chukwuani attempt the spectacular with a shot from outside the box – it is unspectacular and blazes over.

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78 min: Rangers try and work the ball down their left but Hatate clears. A double change for Celtic: Yang and Maeda off; James Forrest and Joel Mvuka are on.

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Updated at 10.40 EDT

76 mins: Moore comes off for Rangers, Nedim Bajrami enters the fray.

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75 min: Gassama wins a corner for Rangers, Trusty with the block once more. Rommens to take – Sinisalo with a confident take.

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Updated at 10.36 EDT