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Ireland 214 (Tector 50, Taijul 5-58) and 286 for 8 (Tucker 108, McBrine 71*, Tector 56, Taijul 4-86, Shakib 2-26) lead Bangladesh 369 (Mushfiqur 126, Shakib 87, Mehidy 55, McBrine 6-118) by 131 runs
Dhaka: Lorcan Tucker became only the second Irishman to hit a Test century as Ireland fought back to lead Bangladesh after day three of the one-off Test.
Ireland looked in danger of an innings defeat after day two in Mirpur when they stood on 27-4 in their second innings - still 155 behind the hosts.
But debutant Tucker made 108 with Andy McBrine unbeaten on 71 as Ireland were 286-8 at the close - a lead of 131.
Harry Tector also struck 56 - his second half-century of the match.
Ireland's revival initially ensured that Bangladesh would have to bat again but the tourists will now believe that they are back in the contest heading into day four.
The Irish will hope that McBrine can continue his brilliant batting which saw him hit eight fours and a six in his 144 balls while tailender Graham Hume was also unbeaten on nine at the close after striking two boundaries.
Wicketkeeper-batter Tucker hit 14 fours and a six in his 162-ball knock and was brilliantly assisted by Tector and McBrine in partnerships of 72 and 111 respectively to put the pressure back on Bangladesh.
Kevin O'Brien is the only other Irishman to notch a Test century, scoring 118 against Pakistan during Ireland's 2018 maiden Test in Dublin.
Tucker believes Ireland's fightback has put them in with a genuine chance of clinching a first Test win after losing their previous matches since they gained Full Member status in 2017.
Tector resumed overnight for a 28-run partnership with Peter Moor before left-arm pacer Shoriful Islam gave the hosts their first breakthrough of the day.
Moor was gone for 16 but Tector and Tucker started the rebuild of the Ireland innings.
Tector eventually departed when he was leg before wicket off Taijul Islam, his 56 making him the first Irish cricketer to hit half-centuries in both innings of a Test match.
Tucker brought up his century with a cover drive for four off left-arm spinner Taijul, raising his bat after hugging McBrine, before falling to the bowling of Ebadot Hossain with Shoriful taking the catch at extra cover.
Mark Adair accompanied McBrine in a 31-run stand before he was removed by Taijul, the most successful Bangladesh bowler of the innings so far with 4-86.
Ireland have lost all three of their previous Tests since becoming a full member of the International Cricket Council in 2017 but will believe they are now in with a chance of a victory that seemed highly improbable after day two.
