Geometry
Problem 1012: Discovering Geometric Concurrency: Proving Perpendicular Intersections in an Equilateral Triangle with
Three Incenters. High School Math Education
The figure depicts an equilateral triangle ABC with a point D. A_{1}, B_{1}, C_{1} represent the incenters of triangles BDC, ADC, and ADB, respectively.
The statement to be proven is that the perpendiculars dropped from A_{1}, B_{1}, and C_{1} to BC, AC, and AB, respectively, intersect at a common point E.
