Centroid

Orthocenter

Circumcircle and circumcenter

Incircle and incenter

Medial triangle

Mid-segment triangle.

Orthic triangle

Pedal triangle

Center of Nine point circle

Nine Point Circle

Trisecting a line segment

Equilateral triangle, given a side

Square, given a side

Triangle Centers with Euler Line

Divide a segment AB into two parts that form a golden ratio.

Hexagon, given a side.

Octagon, given a side.