US-TST 2016 Problem 6

Let $A B C$ be an acute scalene triangle and let $P$ be a point in its interior. Let $A_{1}$, $B_{1}, C_{1}$ be projections of $P$ onto triangle sides $B C, C A, A B$, respectively. Find the locus of points $P$ such that $A A_{1}, B B_{1}, C C_{1}$ are concurrent and $\angle P A B+\angle P B C+$ $\angle P C A=90^{\circ}$.