This is the writeup of Assignment #5 
Brian R. Lawler

EMAT 6680 
10/21/00

1.  Centroid. The CENTROID (G) of a triangle is the common intersection of the three medians.  Given 3 points, construct centroid (G). 
9/25/00

2.  Orthocenter. The ORTHOCENTER (H) of a triangle is the common intersection of the three lines containing the altitudes.  Given 3 points, construct orthocenter (H). 
9/25/00

3.  Circumcenter. The CIRCUMCENTER (C) of a triangle is the point in the plane equidistant from the three vertices of the triangle.  Given 3 points, construct circumcenter (C). 
9/25/00

4.  Circumcircle.  Given 3 points, construct the circumcircle of a triangle. 
10/2/00

5.  Incenter. The INCENTER (I) of a triangle is the point on the interior of the triangle that is equidistant from the three sides.  Given 3 points, construct the incenter of a triangle (I). 
9/25/00

6.  Incircle.  Given 3 points, construct the incircle of a triangle. 
10/2/00

7.  Medial triangle. The MEDIAL TRIANGLE is the triangle connecting the three midpoints of the sides.  Given 3 points, construct a triangle and it's medial triangle. 
10/2/00

7a.  Orthocenter, Midsegment triangle.  Given 3 points, construct the orthocenter. Next, construct the segments connecting each vertex to this orthocenter. Create the triangle formed by the midpoints of these segments. Name this triangle a Midsegment triangle. 
12/12/00

8.  Orthic triangle. The ORTHIC triangle is a triangle connecting the feet of the altitudes of a triangle.  Given 3 points, construct a triangle and its orthic triangle.. 
10/2/00

9.  Pedal triangle. Let triangle ABC be any triangle. Then if P is any point in the plane, then the triangle formed by constructing perpendiculars to the sides of ABC (extended if necessary) locate three points R, S, and T that are the intersections. Triangle RST is the Pedal Triangle for Pedal Point P.  Given 3 points to define a triangle, and a 4th point to be any point on the plane, construct the pedal triangle. 
12/14/00

10.  Center of Nine point circle.  Given 3 points, build a triangle and label the center of the NinePoint circle (N). 
10/2/00

11.  Nine Point Circle.  Given 3 points, build a triangle with it's NinePoint circle. 
10/2/00

12.  Trisecting a line segment.  Given two points, construct and trisect a segment. 
10/2/00

13.  Equilateral triangle, given a side.  Given points AB, construct an equilateral triangle with side lengths AB. 
10/23/00

14.  Square, given a side.  Given points AB, construct a square with side lengths AB. 
10/23/00

15.  Isosceles triangle, given base and altitude.  Construct an isosceles triangle, given base and altitude. The script uses points A, B as the endpoints of the base, and points C, D as the endpoints of a segment defining the length of the altitude. 
10/23/00

16.  Triangle Centers (H, G, C, and I).  Given 3 points, construct G, H, C, and I. 
9/25/00

17.  Triangle Centers with Euler Line.  Given 3 points, construct the Euler line. 
9/25/00

18.  Locus of vertex of a fixed angle that subtends a fixed segment.  ~~UNSOLVED~~  
19.  Divide a segment AB into two parts that form a golden ratio.  Given 2 points, divide a segment at the Golden Ratio. 
10/9/00

20.  Pentagon, given a radius.  Given 2 points: center and vertex, construct a regular pentagon. 
10/9/00

21.  Pentagon, given a side.  Given points AB, construct a regular pentagon with side lengths AB. 
10/23/00

22.  Hexagon, given a side.  Given points AB, construct a regular hexagon with side lengths AB. 
10/23/00

23.  Octagon, given a side.  Given points AB, construct a regular octagon with side lengths AB. 
10/23/00

24.  Tangent lines to two circles.  Given rim, center and rim, center of two circles, construct all tangents to both circles 
10/16/00

25.  Decagon, given a radius.  Given center and vertex, construct a regular 10gon. 
10/9/00

26.  Sublime triangle.  Given 2 points, construct a Sublime triangle. 
10/9/00

27.  2D cube  Given three points, construct a 2D representation of a cube. 
10/23/00

28.  Circle tangent to two circles  Given two circles (actually, define 4 points as pointcenter, pointcenter of two circles), this script will construct a circle tangent to the other two.  12/13/00 
29.  Circle (2nd) tangent to two circles  Given two circles (actually, define 4 points as pointcenter, pointcenter of two circles), this script will construct a different circle tangent to the other two.  12/13/00 
30.  Two Circles tangent to two circles  Given two circles (actually, define 4 points as pointcenter, pointcenter of two circles), this script will construct two distinct circles tangent to the other two.  12/13/00 
31.  Two Circles tangent to two circles  Put 2 points to determine a line and then a pointcenter to determine a circle. This script will construct two circles tangent to the line and the circle.  12/13/00 
Comments? Questions? email me at blawler@coe.uga.edu 
Last revised: December 28, 2000 