by: Doris Santarone

__A Library of GSP Scripts
__

__
__Instead of recreating a construction
over and over again, we can make our lives a little easier using the GSP
scripts feature. They are an efficient way
of repeating constructions. Below
is a library of GSP scripts. For
each construction, I have listed the necessary givens. I have also linked to the
GSP sketch,
where you can use the script.

__
__

1. Centroid –
the centroid, G, of a triangle is the common intersection of the medians of a
triangle.

Given:
Points A, B, and C (vertices of triangle)

2.
Orthocenter – the orthocenter, H, of a triangle is the point of concurrency or the common intersection of the three
**lines** containing the altitudes.

Given:
Points A, B, and C (vertices of triangle)

3. Circumcenter – the circumcenter, C, of a
triangle is the point in the plane equidistant from the three vertices of the
triangle.

Given: Points A, B, and C (vertices of triangle)

4.
Circumcircle – a circle where the center is C,
circumcenter and where the 3 vertices of the triangle lie on the circle.

Given: Points A, B, and C (vertices of triangle)

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: Points A, B, and C (vertices of triangle)

6.
Incircle - a circle where the center is I,
incenter and where the 3 feet of the altitudes of the triangle lie on the
circle.

Given: Points A, B, and C (vertices of triangle)

7.
Medial triangle – the triangle formed by connecting the mid-points of
each side of the triangle.

Given: Points A, B, and C (vertices of triangle)

8.
Orthocenter, Mid-segment triangle – the triangle formed by connecting the
mid-points of the segments from the orthocenter to the vertices.

Given:
Points A, B, and C (vertices of triangle)

9.
Orthic triangle – the triangle formed by connecting the feet of the
altitudes of a triangle.

Given:
Points A, B, and C (vertices of triangle)

10.
Pedal triangle – Given a triangle ABC and any point E in the plane, this
is the triangle formed by the perpendiculars to the sides of ABC.

Given:
Points A, B, and C (vertices of triangle)

11.
Center of Nine point circle – the center of any Nine point circle lies on the corresponding triangle's Euler's line, at the midpoint between that triangle's orthocenter and circumcenter.

Given: Points A, B,
and C (vertices of triangle)

12. Nine Point
Circle - a circle that can be constructed for any given triangle. It is
so named because it passes through nine significant points defined from the triangle. These nine points are:

Given: Points A, B, and C (vertices of triangle)

Given:
Points A and B (to form segment AB)

14.
Equilateral triangle, given a side

Given:
Points A and B (to form one side of the equilateral triangle)

Given:
Points A and B (to form one side of the square)

16.
Isosceles triangle, given base and altitude

Given:
Points A, B, C, and D (Segment AB will be the base, and segment CD will be the
altitude)

17.
Triangle Centers (H, G, C, and I)

Given:
Points A, B, and C (vertices of triangle)

18.
Triangle Centers with Euler Line

Given:
Points A, B, and C (vertices of triangle)

19.
Divide a segment AB into two parts that form a golden ratio

Given:
Points A and B (to form segment AB)

Given:
Points A and B (to form radius of the pentagon)

Given:
Points A and B (to form one side of the pentagon)

Given:
Points A and B (to form radius of the hexagon)

Given: Points A and B (to form one side of the hexagon)

Given:
Points A and B (to form radius of the octagon)

Given: Points A and B (to form one side of the octagon)

26. Triangle, given its medians

Given: Points A and B (to form one median), points C and D (to form a 2nd median), and points E and F (to form a 3rd median).

27. Circle tangent to 2 other Circles

Given: Points A and B (to form circle AB) and points C and D (to form circle CD)

There are 2 constructions to find a circle tangent to circles AB and CD. Below are the 2 options and their respective links.

Click here for the GSP Sketch (including the script).

Click here for this GSP Sketch (and the script).

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