Go Geometry Problems

Dynamic Geometry Problem 974: 'Begonia Theorem', Cevian Triangle, Reflection of a point in a line, Concurrency of Lines. GeoGebra, HTML5 Animation for Tablets (iPad, Nexus). Levels: School, College, Mathematics Education

< PREVIOUS PROBLEM  |  NEXT PROBLEM >

The dynamic figure below shows a triangle ABC and a point D. The triangle A1B1C1 is the cevian triangle of D (cevians AA1, BB1, CC1 concurrent at D). D1, D2, and D3 are the reflections of D in the lines B1C1, A1C1, A1B1. Prove that the lines AD1, BD2, CD3 are concurrent at E, called "begonia point". Reference: Darij Grinberg, Begonia points and coaxal circles.
See also: Kaleidoscope of Problem 974 base on Poincare Disk Model.

Dynamic Geometry of Problem 974
The interactive demonstration above was created with GeoGebra.

To stop/play the animation: tap the icon in the lower left corner.
To reset the interactive figure to its initial state: tap the icon in the upper right corner.
To manipulate the interactive figure: tap and drag points or lines.
  

GeoGebra
GeoGebra is free and multi-platform dynamic mathematics software for all levels of education that joins geometry, algebra, tables, graphing, statistics and calculus application, intended for teachers and students. Many parts of GeoGebra have been ported to HTML5. It has received several educational software awards in Europe and the USA.
 

   Dynamic Geometry Problem 974: 'Begonia Theorem', Cevian Triangle, Reflection of a point in a line, Concurrency of Lines. GeoGebra, HTML5 Animation for Tablets
 


 

Home | SearchGeometry | Problems | All Problems | Open Problems | Visual Index | 10 Problems | Problems Art Gallery Art | 971-980 | Dynamic Geometry | GeoGebra | Triangles | Concurrent lines | Reflection | iPad Apps | Nexus 7 Apps | Projects | Email | Solution/Comment | by Antonio Gutierrez