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. A1, B1, C1 represent the incenters of triangles BDC, ADC, and ADB, respectively.
The statement to be proven is that the perpendiculars dropped from A1, B1, and C1 to BC, AC, and AB, respectively, intersect at a common point E.