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