Some interesting tools

Triangle Centers

Centroid : the center of mass of a triangle

centroid and circumcircle: This tool constructs the centroid and the circumcircle of a given triangle

Orthocenter: The point of intersection of the three altitudes of a triangle

Circumcenter: The circumcenter is the center of a triangle's circumcircle. It can be found as the intersection of the perpendicular bisectors.

Circumcircle: is the circle that passes through all vertices of a triangle and contains the entire figure in its interior

Incenter: is the center of the incircle for a given triangle. It can be found as the intersection of angle bisectors, and it is the interior point for which distances to the sides of the triangle are equal. It has trilinear coor

incenter and incircle: The largest possible circle that can be drawn interior to a plane figure

Triangle centers: triangle's orthocenter, centroid, and circumcenter

Euler line: The line segment that passes through a triangle's orthocenter, centroid, and circumcenter. These three points are collinear for any triangle. In addition, the distance from the orthocenter to the centroid is twice the distance from the circumcenter to the centroid.

Nine-point circle: Also called Euler's circle or the Feuerbach circle, is the circle that passes through the perpendicular feet, and dropped from the vertices of any reference triangle on the sides opposite them. Euler  showed that it also passes through the midpoints of the sides of the triangle. By Feuerbach's theorem, the nine-point circle also passes through the midpoints of the segments that join the vertices and the orthocenter . These points are commonly referred to as the Euler points.

Mid point segment: This tool constructs the midpoint of a segment

Trisection of a segment

Medial triangle: the triangle constructed using the midpoints of each side of a given triangle

Polygons

equilateral triangle: A triangle with three congruent sides

Square A rectangle with all four sides of equal length. Formally, a square is a quadrilateral with four congruent sides and four congruent angles

pentagon given radios

Regular Hexagon: A polygon for which all sides are congruent and all angles are congruent.