The Department of Mathematics Education


Personal Library of GSP Scripts

by GooYeon Kim


1. CENTROID : The common intersection of the three medians of a triangle. A median of a triangle is the segment from a vertex to the midpoint of the opposite side.
 
SCRIPT of Centroid


2. ORTHOCENTER (H) : The common intersection of the three lines containing the altitudes of a triangle.

 
SCRIPT of Orthocenter
 


3. CIRCUMCENTER (C) : The point in the plane equidistant from the three vertices of a triangle. Since a point equidistant from two points lies on the perpendicular bisector of the segment determined by the two points, C is on the perpendicular bisector of each side of the triangle. It is the center of the CIRCUMCIRCLE.

 
SCRIPT of Circumcenter
 


4. INCENTER (I) : The point on the interior of a triangle that is equidistant from the three sides. Since a point interior to an angle is equidistant from the two sides of the angle lies on the angle bisector, then I must be on the angle bisector of each angle of the triangle. It is the center of the INCIRCLE (the inscribed circle) of the triangle.

SCRIPT of Incenter

 


5. MEDIAL triangle : The triangle connecting the three midpoints of the sides of a given triangle.

 

SCRIPT of the Medial triangle

 


6. ORTHIC Triangle : The triangle connecting the feet of the altitudes of any acute triangle.

ORTHIC triangle 1

ORTHIC triangle 2

SCRIPT of Orthic triangle

 


7. Let triangle ABC be any triangle. Then if P is any point in the plane, then the triangle formed by constructing perpendiculars to the sides of ABC locate three points R, S, and T that are the intersections. Triangle RST is the PEDAL Triangle for Pedal point P.

PEDAL Triangle1 :

PEDAL Triangle 2

SCRIPT of Pedal Triangle

 


8. SCRIPT of NINE POINT CIRCLE

 

 


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