| 1.centroid |
The centroid is located at the intersection of the medians of each side of the triangle. |
| 2.Orthocenter |
The orthocenter is located at the intersection of the altitudes of each side of the triangle. |
| 3.Circumcenter |
The circumcenter is located at the intersection of the perpendicular bisectors of each side of the triangle. |
| 4.Circumcircle |
The circumcircle has a center at the circumcenter and passes through each vertice of the triangle. |
| 5.Incenter |
The incenter is located at the intersection of the angle bisectors of the triangle. |
| 6.Incircle |
The incircle has a center at the incenter of the triangle, with a radius being the perpendicular distance from the incenter to each side of the triangle. |
| 7.Medial triangle |
The medial triangle has vertices at the midpoint of each side. |
| 8.Orthocenter, Mid-segment triangle |
The vertices of the ortho mid-segment triangle are located at the midpoint of the segment that connects the orthocenter to each vertex of the original triangle. |
| 9.Orthic triangle |
The orthic triangle's vertices are located at the foot of each altitude on each side of the original triangle. |
| 10.Pedal triangle |
A pedal triangle is made by selecting a point P and creating the perpendiculars from each side to that point P. The vertices of the pedal triangle are located where the created perpendiculars intersect each side. |
| 11.Center of Nine point circle |
The center of the nine point circle is at the mid point of Euler's line,the segment formed by the orthocenter and the circumcenter. |
| 12.Nine point circle |
The nine point circle is formed using the midpoints of each side of a triangle, the foot of each altitude of the triangle, and the midpoint of the segment from the orthocenter to each vertex of the triangle. |
| 13. |
Trisecting a line segment cuts a given line segment into three equal parts. |
| 14.Equilateral triangle, given a side |
Given a line segment, an equilateral triangle is made up of all three sides equal to the line segment. |
| 15.Square, given a side |
Given a line segment, a square is made up of all four sides equal to that line segment. |
| 16.Isosceles triangle, given base and altitude |
Given a base length and altitude, create an isosceles triangle. |
| 17.Triangle centers (H, G, C ,and I) |
Given a triangle, finds the orthocenter (H), centroid (G), circumcenter (C), and incenter (I). |
| 18.Triangle centers with Euler Line |
Given a triangle, finds four centers of the triangle (H, G, C, I) which connect to form the Euler Line. |
| 19.Locus of vertex of a fixed angle that substends a fixed segment |
Given a fixed angle, find the locus of the vertex. |
| 20.Divide a segment AB into two parts that form a golden ratio |
Given a segment, divide the segment into the golden ratio. |
| 21.Pentagon given a radius |
Given a radius, construct a pentagon. |
| 22.Pentagon given a side |
Given a side length, construct a pentagon. |
| 23.Hexagon given a side |
Given a side, construct a hexagon. |
| 24.Octagon given a side |
Given a side, construct an octagon. |
| 25. tangent circles |
tangent circles, one inside the other |
| 26.Tangent Circles |
tangent circles, overlapping |
| 27.Tangent Circles |
tangent circles, disjoint |
