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.