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Celtic will face Rangers in the Scottish Cup semi-finals after seeing off a battling Dundee United.

The striker grabbed a late second goal, helping on an effort from substitute Karamoko Dembele.

United pressed valiantly but posed little threat in attack at Tannadice.

The win stretches the Scottish Premiership leaders’ run of unbeaten domestic games to 30.

Celtic, who have lifted the cup a record 40 times, join Rangers, Hearts and Hibernian in the last four – the first time the Glasgow and Edinburgh clubs have all made it this far together.

And, with the League Cup already in the trophy room and a three-point lead in the league, fans’ thoughts will be turning to a potential fifth treble in six seasons.

Amid the early hustle and bustle, Celtic forward Daizen Maeda brushed the roof of the net from a long way out.

The breakthrough came on 12 minutes when McGregor ran on to a short corner and let fly from the edge of the penalty area. Nicky Clark stuck a leg out in an attempt to block, but only succeeded in diverting the ball away from Siegrist.

The goal knocked the stuffing out of the home side for a while, as did the loss of energetic midfielder Ian Harkes to injury, but a wild challenge from Reo Hatate on Kieran Freeman reignited United after half an hour.

However, an increase in aggression and work-rate did not stem the flow of Celtic attacks and there was a moment of controversy when the visitors thought they had scored a second goal.

Maeda squeezed a shot in from close range but the ball had come his way via the arm of Giakoumakis. It wasn’t a deliberate action from the Greek, with the changed rulebook therefore suggesting the goal should have stood.

Soon after, McGregor sent a fizzing effort just wide of the top corner and a swivelling Giakoumakis then volleyed off target.

The hosts continued to graft commendably after the interval, although they were undone by too many errant passes.

Just when it looked like Celtic had been knocked off their stride, they were handed a gift by Siegrist, who fumbled a cross from Maeda at the feet of Giakoumakis and the striker could not miss.

Thereafter, Ange Postecoglou’s side managed to keep United at bay without too much fuss and found a late goal when Dembele’s deflected shot looped up nicely for Giakoumakis to nudge home.

Man of the match – Callum McGregor