Problem 1012: Equilateral Triangle, Incenters,
Inscribed Circles, Perpendicular, Concurrent Lines.
Level: School, College
The figure shows an equilateral triangle ABC with a point D. A1, B1, C1 are
the incenters of triangles BDC, ADC, and ADB, respectively. Prove that
the perpendiculars dropped from A1, B1, and C1 to BC, AC, and AB,
respectively, are concurrent at a point E.