MathNet 2020 — Math Olympiad Vault — Part 04 Question 144

Fix an equilateral triangle $ABC$. For every line $l$ through $B$, let $D_l,E_l$ be the perpendicular projections of $A,C$ onto $l$. Determine the locus of points $P_l$ for which $P_lD_lE_l$ is equilateral.