# Assignment #5

## The Library of Scripts

### Introduction

In this write-up I present my Library of GSP Scripts. Scripts are useful tools for performing frequently used constructions when provided with a minimal amount of given information. For each of the scripts provided, I will identify the givens required.

### Segments of Equal Length

• Trisecting A Segment - Given the endpoints of the segment and a random point not on the segment.
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• Golden Ratio Segment (Divides segment into two portions that form a golden ratio) - Given the endpoints of the segment.

• ### Centers of Triangles

• Orthocenter - O - Given the three vertices of the triangle.
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• Incenter - I - Given the three vertices of the triangle.
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• Triangle Centers (Orthocenter - H, Centroid - G, Circumcenter - C, and Incenter - I) - Given the three vertices of the triangle.
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### Circles of Triangles

• Incircle - Given the three vertices of the triangle.
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### Triangles of Triangles

• Orthic Triangle - Given the three vertices of the triangle.
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(The triangle formed from the midpoints of the segments from the vertices to the orthocenter)

• Pedal Triangle - Given the three vertices of the triangle and a distinct point P, the Pedal Point.

### Polygons

• Isoceles Triangle - Given the endpoints of the base and the endpoints of a segment representing the desired altitude.

• Square - Given the endpoints of one side.

• Pentagon - Given the endpoints of one side.

• Pentagon - Given the endpoints of a radius.

• Hexagon - Given the endpoints of one side.

• Octagon - Given the endpoints of one side.

• Dodecagon - Given the endpoints of one side

### Other Constructions

• Arc of Circle - Locus of the vertices of a fixed angle that subtends a fixed segment - Given the vertex of the angle and the endpoints of the fixed segment it subtends.

• Tangent Circle 1 - Construct a circle externally tangent to two other circles given the centers of the two circles and a point on each circle.

• Tangent Circle 2 - Construct two circles tangent to a circle and a line given two points on the line, the center of the circle and a point on the circle.