Linked from
The 20 pages that link to Incenter, each with the reason it gives.
Euler lineRelated: It is a familiar triangle center that generally does not lie on the Euler line.
Euler's inequalityRelated: It is the center of the incircle whose radius appears in the inequality.
Equal Incircles TheoremRelated: It is the center of the incircle whose radius the theorem compares.
Erdős–Mordell inequalityRelated: At this point, equality holds in the Erdős–Mordell inequality.
Incenter–excenter lemmaRelated: It is the interior center named in the lemma.