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Geometry Problem 886: Right Triangle, Incenter, Angle Bisector, Perpendicular, 45 Degrees, Concyclic Points, Isosceles Right Triangle. GeoGebra, HTML5 Animation for Tablets (iPad, Nexus). Levels: School, Mathematics Education

In a right triangle ABC, I is the incenter, AE and CD are the bisectors of angles A and C. DF and EG are perpendicular to AC. AE meets BF and BG at H and J, CD meets BG and BF at L and K. Prove that (1) angle FBG = 45 degrees; (2) B, J, I, K are concyclic points; (3) F, H, I, L, G are concyclic points; (4) triangle FIG is an isosceles right triangle.
 


 

Dynamic Geometry of Problem 886
The interactive demonstration above was created with GeoGebra.
 

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.
 

Right Triangle, Incenter, Angle Bisector, Perpendicular, 45 Degrees, Concyclic Points, Isosceles Right Triangle. GeoGebra, HTML5 Animation for Tablets (iPad, Nexus)

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