Video examples (OK Geometry Plus)

Example 2. (OK Geometry Plus)

The circle k touches inwardly two sides of the triangle ABC triangle and its circumcircle.

• Create the configuration in Sketch Editor. (video.mp4)
• Find a Euclidean construction of the circle k. (video mp4)
• Observe how the radius rk of the circle k is algebraically related to the quantities of triangle ABC. (video mp4)
   

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)