Kerry and Armagh have won three of the last four All-Irelands between them
Armagh will face Kerry and Donegal will travel to Dublin in the third round of the All-Ireland Senior Football Championship.
Kieran McGeeney's side. who were stunned by Louth in Inniskeen in Round 2A, will travel to the holders as the last two winners of the All-Ireland will go head-to-head in a bid to reach the quarter-finals.
Kerry were in the third round courtesy of their Round 2B win over Kildare.
After their loss to Cork. Jim McGuinness' Donegal face a difficult third-round tie away to Dublin, who beat Cavan on Sunday.
Monaghan will take on Westmeath and Mayo will host Meath in the other round three matches.
The winners of those ties will reach the quarter-finals. join Tyrone, Cork, Galway and Louth, who have already qualified for the last eight.
There is guaranteed to be an Ulster county in the final of the Tailteann Cup after Down were drawn with Fermanagh in the last four.
The game will take place at Croke Park on Saturday, 20 June,. the winner will face either Offaly or Wicklow in the decider.
All-Ireland round three - ties to be played on 20 and 21 June
Monaghan v Westmeath
Tailteann Cup semi-finals - played at Croke Park on Saturday, 20 June
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