Which crusader state was established in 1109 with Tripoli as its capital?

The crusader state established in 1109 with Tripoli as its capital was the County of Tripoli.

The county was one of the four principal Crusader states created in the Levant after the First Crusade. Its territory occupied parts of modern northern Lebanon and western Syria. Although Tortosa served as an early capital from 1102 to 1109, the capture of Tripoli in 1109 made that city the county’s political centre for the remainder of its existence.

Bertrand of Toulouse became the first count of Tripoli after the city fell. The county was formally connected to the wider Latin Christian political world, but its rulers often had to balance relationships with the Kingdom of Jerusalem, the Principality of Antioch, local Christian communities, and neighbouring Muslim powers.

The other options were separate states: Edessa was the County of Edessa, Antioch was a principality, and Jerusalem was a kingdom. The County of Tripoli survived longer than several other Crusader states, but it was conquered by the Mamluk sultanate in 1289 under Sultan Qalawun.