Math
Geometry
Problem 1012: Equilateral Triangle, Incenters,
Inscribed Circles, Perpendicular, Concurrent Lines.
Level: School, College
The figure shows an equilateral triangle ABC with a point D. A_{1}, B_{1}, C_{1} are
the incenters of triangles BDC, ADC, and ADB, respectively. Prove that
the perpendiculars dropped from A_{1}, B_{1}, and C_{1} to BC, AC, and AB,
respectively, are concurrent at a point E.
