Rayen Antillanca.
Assignment 5
This
page contains a library of GPS script tool. The idea is to use many times and
efficient these tools.
1.
Centroid 
The
centroid (G) of a triangle is the point where
the three medians intersect. 
2.
Orthocenter 
The
orthocenter (H) of a triangle is
the point where the three altitudes of the triangle intersect. 
3.
Circumcenter 
The
circumcenter (C) of a triangle is the point in
the plane equidistant from the three vertices of the triangle. 
4.
Circumcircle 
The
circumcircle
of a triangle is a circumscribed circle that passes three vertices of the
triangle, and its center is the circumcenter. 
5.
Incenter 
The
incenter (I) of a triangle is the point on the
interior of the triangle that is equidistant from the three sides. 
6.
Incircle 
The
incircle
of a triangle is an inscribed circle whose center is the incenter. 
The
medial triangle is a triangle with
vertices as the midpoints of the triangle. 

The
midsegment triangle is a triangle
that is formed by midsegments of a triangle, which are the lines segments
joining midpoints of two sides of a triangle. 

The
orthic triangle is a triangle joining the
feet of the altitudes of the triangle. 

10.
Pedal triangle 
The
pedal triangle is a triangle whose
vertices are the feet of perpendiculars from each vertex of the triangle to
their opposite sides in the triangle. 
The
center of nine point circle is the
center of the nine point circle. 

The
nine point circle is a circle that
passes through nine significant points, six lying on the triangle itself
(unless the triangle is obtuse). They include:


This
tool is how to draw trisecting
points of a line segment. 

The
equilateral triangle is a triangle
that has three congruent sides. This tool is how to draw an equilateral triangle with given side. 

The
square is a quadrilateral that has
four congruent sides and four congruent angles. This tool is how to draw a square with given side. 

The
isosceles triangle is a triangle
that has two congruent sides. This tool is how to draw an isosceles triangle
with given base and altitude. 

The
four centers of triangles are orthocencer (H), centroid (G), circumcenter (C), and incenter (I). 

The
Euler Line of a triangle is a line
that passes the Center of nine point circle, the Circumcenter
(C), Centroid (G), and Orthocenter(H)
of the triangle. 

19.
Locus of vertex of a fixed angle that
subtends a fixed segment 
This
is how to draw a locus of the vertex of a fixed angle that subtends
a fixed segment. 
20.
Divide a segment AB into two parts that
form a golden ratio 
A
golden ratio of a line segment is
the ratio that is the length of the larger portion of the line segment to the
length of the whole line segment. The golden
ratio which is named . ( ) 
The
pentagon is a polygon that has
five sides. This tool is how to draw a pentagon
with given radius. 

The
pentagon is a polygon that has
five sides. This tool is how to draw a pentagon
with given side. 

The
hexagon is a polygon that has six
sides. This tool is how to draw a hexagon
with given side. 

The
octagon is a polygon that has
eight sides. This tool is how to draw an octagon
with given side. 

Circle tangent to the two circles with one point of tangency being the
designated point. 

This animation draws a locus
of a tangent
circle to the two circles with one point of tangency being the designated point when it does
not surround the inside circle 

This animation draws a locus
of a tangent
circle to the two circles with one point of tangency being the designated point when it does
surround the inside circle 

This animation draws
the locus of the circles (when it does not surround the inside circle and when
it does surround the inside circle) which are
tangent two circles with one point of tangency being the designated point. 

29.
Locus of a tangent circle two circles
intersect to each other 
This animation draws the locus of the circles (when it does
not surround the inside circle and when
it does surround the inside circle) which are
tangent two circles with one point of tangency being the designated point
when these two circles are intersected. 
30.
Locus of a tangent circle two circles are
separate to each other 
This animation draws the locus of the circles (when it does
not surround the inside circle and when
it does surround the inside circle) which are
tangent two circles with one point of tangency being the designated point
when these two circles are separated. 
Note: All tools on this web page were made with The Geometer’s
Sketchpad 