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Square, given a side

Pedal triangle

Orthocenter

Orthic triangle

Orthocenter, Mid-segment triangle

Incircle

Incenter

Circumcenter

Centroid

Medial Triangle

Circumcircle

Trisecting a line segment

Isosceles Triangle, given a base and altitude

Triangle Centers (O, C, CC, CC(=H),I)

Euler Line