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
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The dynamic figure below shows a triangle ABC and a point D.
The triangle A_{1}B_{1}C_{1} is the cevian triangle of D (cevians AA_{1}, BB_{1}, CC_{1} concurrent at D). D_{1}, D_{2}, and D_{3} are the reflections of D in the lines B_{1}C_{1},
A_{1}C_{1}, A_{1}B_{1}. Prove that the lines AD_{1}, BD_{2}, CD_{3} 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.
