Circumcenter Centriod   Incenter
Orthocenter   all four points together
Angle bisector instructions   Perpendicular bisector instructions
Median instructions    Altitude instructions
Period 3     Period 4     Period 5

Instructions for constructing an angle bisector.
The circles represent the arcs.
Create the intersections that you see here.
Start with an arc from the vertex "A" though the two rays (red circle) to create the intersections at "D" and "E".

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Next use center "E" and radius "ED" to construct another arc (pink).
Note the radius of the pink circle is the distance between the two points "E" and "D", on the rays.

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Next use center "D" and radius "DE" to construct another arc (blue).
Note the radius of the blue circle is the distance between the two points "D" and "E", on the rays.

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Notice that this has created another intersection point "F".
Use the vertex "A" and the intersection of the pink and blue circles "F" to construct the angle bisector (green).

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Yahoo!  You have constructed an angle bisector.
Now do the same thing at another angle.
Good luck!

Circumcenter  Centriod Incenter
Orthocenter   all four points together
Period 3     Period 4     Period 5