MathNet 2023-part-04 — 191 problems (EN–VI) Question 187

Let $ABC$ and $DEF$ be two congruent equilateral triangles, centered at $O_1$ and $O_2$, respectively, such that segment $AB$ meets segments $DE$ and $DF$ at $M$ and $N$, respectively, and segment $AC$ meets segments $DF$ and $EF$ at $P$ and $Q$, respectively. The bisectors of angles $EMN$ and $DPQ$ meet at $I$, and the bisectors of angles $FNM$ and $EQP$ meet at $J$. Prove that $IJ$ is the perpendicular bisector of the segment $O_1O_2$.

Bogdan Maxim