The following are scripts in GSP. To construct the given object:

1. open the script by clicking on the name

2. select required obejects (points, segments, etc.). Use a new sketch if you desire.

3. play script

**centroid
(G)**: the point where the medians
of a triangle intersect.

**orthocenter
(H)**: the point where the lines
containing the altitudes of a triangle intersect.

**circumcenter
(C)**: the center of the circle that
contains the the vertices of a triangle. The vertices are equidistant
from the circumcenter. The circumcenter is the intersection point
of the perpendicular bisectors of the the sides of a triangle.

**circumcircle**: the circle "around" a triangle. The circumcircle
passes through the vertices of the triangle. The center is the
circumcenter of the triangle.

**incenter
(I)**: the center of the circle "inside"
a triangle; that is, the circle within the triangle that is tangent
to the sides of the triangle. The incenter is equidistant from
the sides of the triangle. The incenter is the intersection point
of the angle bisectors of the triangle.

**triangle
centers (H, G, C, I)**: orthocenter,
centroid, circumcenter, and incenter of a triangle.

**triangle
centers with the Euler line**: The
Euler line is the line which contains H, G, and C of a triangle.

**medial
triangle**: a triangle formed by
connecting the midpoints of a triangle.

**orthocenter/midsegment
triangle**: The midsegment triangle
is the triangle whose vertices are the* midpoints* of the
segments formed by connecting each of the vertices of a triangle
and the orthocenter H (In triangle ABC: the midpoints of AH, BH,
and CH form the vertices of the midsegment triangle.).

**orthic
triangle**: the triangle whose vertices
are the the feet of the altitudes of a triangle.

**pedal
triangle**: given a triangle ABC
and an arbitrary point P. Let R, S, and T be the feet (intersection
points) of the lines through P which are perpendicular to the
lines containing the sides of triangle ABC. R, S, and T are the
vertices of the pedal triangle.

**nine
point circle**: a circle (associated
with any triangle) which passes through the three midpoints of
the sides, the three feet of the altitudes, and the three vertices
of the midsegment triangle.

Given a side:

isosceles triangle(given base and altitude)

pentagon

Given a radius:

pentagon

divide a segment into two parts that form the golden ratio

locus of the vertex of a fixed angle that subtends a fixed segment