'Contae' is masculine so 'h' in Cill Dara in TG. 'Foireann' is feminine so why the 'h'? What simple thing am I missing?

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Placenames like Cill Dara function as a block and the genitive is indicated by leniting the first letter, where possible, irrespective of the gender of the noun they modify:

Cuan Bhaile Átha Cliath;
oibrithe Bhéal Feirste

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Múinteoir Gaeilge - Irish Teacher
My "specialty" is Connemara Irish, particularly Cois Fhairrge dialect, but I can also speak Ulster and Munster Irish with native-level pronunciation.
Is fearr Gaeilge ḃriste ná Béarla cliste, cinnte, aċ i ḃfad níos fearr aríst í Gaeilge ḃinn ḃeo na nGaeltaċtaí.
Gaeilge Chonnacht (GC), go háraid Gaeilge Chois Fhairrge (GCF), Gaeilic Uladh (GU), Gaelainn na Mumhan (GM), agus Gaeilge an Chaighdeáin Oifigiúil (CO).

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