Advanced commands

Scenes and HTML animated presentations

Here show how to create and use scenes in constructions. For this purpose we use the Lucas circles of triangles. The figure show a triangle ABC with an inscribed square along the side BC. The A-Lucas circle of ABC passes through A and the two vertices of the square not laying on BC.

How to use scenes to show the construction steps for A-Lucas circle. (video.mp4)
How to use scenes to show some observed properties of the A-Lucas circle. (video mp4)
How to use scenes to show objects added to Lucas circles. (video mp4)
How to visualise scenes in the construction view (video mp4).
How to visualise and comment scenes in the project view (video.mp4).
How to create a HTML report with animated figures (video.mp4).
To create a report showing scenes as figures use the report style Scenes (mosaic).

Example 3. (OK Geometry Plus)

Given is a triangle ABC. Let ka, kb, kc be the circles inscribed in the regions between incircle of ABC an the respective pairs of sidelines through A, B, C. Let k be the circle internally tangent to ka, kb and kc and let A', B' C' be the points of contact of circles ka, kb, kc and k. It turns that the lines AA', BB' and CC' concur at a point P.

Create the cyclic construction in Sketch Editor. (video.mp4)
Analyse the position of the point P in the reference triangle ABC.. (video mp4)
Observe the trilinears of the point P in the reference triangle ABC.. (video mp4)

Example 4. (OK Geometry Plus)

Given is a triangle ABC and a point P. Let AA', BB', CC' be Cevian lines all three passing through P.
For what position (if any) of the point P are the line segments AA', BB', CC' congruent?
What is the length of the line segments in such a case?

Create the configuration by implicit construction. (video mp4)
Analyse the position of the point P in the reference triangle ABC. (video.mp4)
Observe how is the length of the segments AA', BB', CC' algebraically related to the quantities of triangle ABC. (video mp4)