Video examples (OK Geometry Basic)

Example 1. (OK Geometry Basic)

A circle k' touches internally a circle k of diameter AB at point B. Furthermore, the line p passes through A and touches the circle k' at point C.
How to construct the circle k'' that
- touches the line p in the interior of the segment AC,
- touches internally the circle k,
- touches externally the circle k' ? 

If p, p', and p'' are the three common tangents to k' and k'', then construction of these tangents is obviously the solution to our problem.
  • Create the configuration using commands for difficult objects (video mp4).
  • Observe the properties (video mp4).
  • Create a project of hypothetised properties (video mp4).
     

Example 2. (OK Geometry Basic)

Given is an acute triangle ABC.
For a point P on the side BC consider the projections B' and C' of P onto the sides AB and AC respectively.
Hypothetise, where to position the point P so that the sum of the areas of triangles PB'B and PC'C is minimal?
 
  • Create the non optimised configuration in Sketch Editor. (video.mp4)
  • Observe the optimal position for the point P that minimises the considered areas. (video mp4)

Example 3. (OK Geometry Basic)

Given is a triangle ABC.
Where to position a point P on the plane so that the orthogonal projections A', B', C' of P onto the sidelines BC, CA and AB form an equilateral triangle A'B'C'?
Find a plausible hypothesis for the solution.
 
  • Create a 'false' configuration in which A'B'C' is not equilateral. (video.mp4)
  • Use implicit construction command to position the point P. Then analyse the configuration. (video mp4)

Example 4. (OK Geometry Basic)

Given is a triangle ABC and its incentre I. Let A' be the mirror image of I in the sideline BC. Define B' and C' cyclically. Let A'', B'', C'' be the mirror images of A, B, C in the incentre I.
You can observe that the lines AA', BB', CC' concur in a point (the centre X79 of ABC).
Similarly, the lines A'A'', B'B'', C'C'' concur in a point (the centre X7972 of ABC).
  • Create the configuration using transformations of single or multiple objects. Then analyse the configuration. (video mp4)