Nagel Point of the Medial Triangle = Incenter.

Nagel Point of the Pedal Triangle of the Circumcenter = Incenter.

Nagel Point of the Cyclocevian Triangle of the Orthocenter = Incenter.

Nagel Point of the Half-cevian Triangle of the Centroid = Spieker Center.

Nagel Point of the Medial Triangle of the Medial Triangle = Spieker Center.

Nagel Point of the Orthic Triangle of the Circum-Incentral Triangle = Spieker Center.