MathNet 2024-part-04 — 168 problems (EN–VI) Question 147

Let $\triangle ABC$ be a triangle. Prove that the orthogonal projections of the point $A$ on the external bisectors of the angles $B$ and $C$, the orthogonal projections of the point $B$ on the external bisectors of the angles $A$ and $C$, and the orthogonal projections of the point $C$ on the external bisectors of the angles $A$ and $B$ are concyclic.

Petru Braica