Circles: SketchPad Files
(1). On opening any of these scripts enclosed in the above pages you may not actually see them! - What you may see instead is a blank Sketch File probably called "Sketch01.gsp". If you are unfamiliar with SketchPad all that you need to do is to click on the "Restore" Button in the top right of the active Sketch file Window Toolbar.
(2). All of these filenames in this page are LONG! - Therefore, if you want to preserve these (Because Version 3.* of SketchPad does not use long filenames) you must either RIGHT-CLICK on the file links within the above directories and then choose "Save Target As...". This allows you to save the file directly to a disk/drive or after using a LEFT-CLICK select the "Save this file to disk" Option Box rather than selecting the "Open this file from its current location". If you choose this last option then Geometer's SketchPad will automatically open - if you have it! - but then after viewing the file if you then try to save it you will not be able to use a long filename.
D - All Three Excircles
Starting with 3 Points this script constructs all Excircles.
- CCCL (Circles ARE present at start) Tangent Script.gss
Starting with 2 circles and a line where each circle is tangential to the line and to one another this script draws a third circle tangential to both the line and the other 2 circles.
- CCCL (Circles NOT present at start) Tangent Script.gss
Starting with a point and a line with a point on it, this script draws 3 circles each tangential to the line and one another.
D - CCL Tangent Script.gss
Starting with a point and a line with a point on it, this script draws 2 circles each tangential to the line and one another.
D - Centre of any Arc.gss
This script constructs the centre of curvature of an Arc if (for whatever reason) it is not present. Only the Arc needs to be selected - no points need be present to run the script.
D - Circle Through 3 Points.gss
Use any three points through which to draw a circle (For whatever reason SketchPad will only construct an Arc through 3 such points)
D - Circumcircle Script.gss
This script constructs the Circumcircle and Circumcentre given the 3 vertices of any triangle. It is not necessary to have the triangle present to run the script.
D - External
Tangents to Two Circles.gss
This script constructs both External Tangents to any two Circles
D - Incentre and Circumcentre Construction.gss
This script constructs both Incircle, Incentre and Circumcircle, Circumcentre given the 3 vertices of any triangle. It is not necessary to have the triangle present to run the script.
D - Incentre Script.gss
This script constructs the Incircle and Incentre given the 3 vertices of any triangle. It is not necessary to have the triangle present to run the script.
D - Internal Tangents to Two Circles.gss
This script constructs both Internal Tangents to any two Circles
D - Nine Point Circle Centre Construction.gss
Constructs the Centre Point of the Nine Point Circle given the 3 vertices of any triangle. It is not necessary to have the triangle present to run the script.
D - Nine Point Circle Construction and Full Labelling.gss
Constructs the Nine Point Circle and its associated Points given the 3 vertices of any triangle. It is not necessary to have the triangle present to run the script.
D - Single Excircle Script.gss
Starting with 3 Points this script constructs a single Excircle.
D - Single Tangent Circle to Two Circles.gss
Given any two Circles, this script constructs a third circle that is Tangential to the original circles. The centre of this tangent circle leaves its trace locus as the circle is dragged.
D - Tangent Circle Pair to Two Circles.gss
Given any two Circles, this script constructs 2 tangent circles to the original circles. The centres of these tangent circles leave trace locii as the circles are dragged.
D - Tangents from a Point to a Circle.gss
This script construct two tangents from any exterior Point to a given Circle.
D - Two Circles through two points and tangential to a line.gss
This script draws two Circles that pass through two given Points which are also both tangential to a given Line.
D - A Constant Chord Theorem.gsp
In this sketch drag T to see the chord properties
D - All Apollonius' Circles in a Triangle.gsp
D - Apollonius' Circle.gsp
D - Apollonius' Line.gsp
D - Arbelos.gsp
D - CCCCCCCCC Circle-Line Tangencies.gsp
Eight Circles Tangential to one Line - Further Circles are easily added using the script D - CCCL (Circles ARE present at start) Tangent Script.gss given above.
D - Chord Properties.gsp
A Button driven dynamic experimental investigation of two Chord Theorems.
D - Circle Tangencies to 3 Circles.gsp
Starting with the three red circles that can be dragged and resized this Sketch shows all of the possible (blue) tangent circles that can be drawn to the original three. Not one of my making but a stunning demonstration by Paul Kunkel. See the excellent explanation at his Web Page and many more GSP files.
D - Conics from Inner and Outer tangent circles to 2 circles.gsp
In this sketch the blue circles are fixed and the red and blue circles are moving tangent circles whose centres trace out conic locii.
D - Eight Point Circle Sketch.gsp
This sketch can be built up slowly with Hide/Show Buttons showing fully all the steps in the construction.
D - Euler Line Sketch - Showing Vectors.gsp
Another property of this remarkable Line between centres.
D - Exterior Tangent Circle Centre Loci (Conics).gsp
The red Tangent Circle moves around the two black Circles. Its centre traces out the Loci of a Conic.
D - Excircle Theorem.gsp
A interesting and surprising result regarding circles constructed from Excircle centres and the incentre of any triangle ABC.
D - Feuerbach's Theorem.gsp
An amazing Theorem regarding Tangency properties of the Nine Point Circle.
D - Interior Tangent Circle Centre Loci (Conics).gsp
The red Tangent Circle moves around within the two black Circles. Its centre traces out the Loci of a Conic.
D - Johnson's Theorem.gsp
An interesting circle theorem that states that if three equal sized circles intersect at a point then a similar sized (Blue) Circle passes through their second points of intersection with each other. This is most easily seen on using Inversion Theory on any Triangle (With sides extended) and its associated Circumcircle.
D - Miquel's Theorem.gsp
Another interesting theorem that can be directly linked to Miquel's Triangle in my SketchPad Triangle page using Inversion Theory. Try using either file and invert using the Inversion Scripts on my Inversions Page after first drawing in a Circle of Inversion of your own choosing.
D - Monge's Theorem - Concurrent Tangent Intersections.gsp
A nice Concurrency Theorem regarding Circle Tangent Lines
D - Nine Point Circle - Area Comparison with Circumcentre.gsp
A complete Sketch of the Nine Point Circle.
D - Nine Point Circle Sketch with Full Labelling.gsp
Another animated Nine Point Circle.
D - Orthogonal Circle to Three Other Circles.gsp
A Radical Axes construction for Orthogonal Circles.
D - Pivot Theorem.gsp
Drag to see angle properties in this Theorem
D - Reflect a General Point P onto Triangle Sides.gsp
An interesting Circle Theorem based on reflections
D - Six Circles Theorem in a Triangle.gsp
A very nice Circle Tangency Theorem.
D - Three-Circle Tangent-Coaxial Property.gsp
An interesting Tangency condition to two circles.