Problem

Source: Kyiv City MO 2022 Round 2, Problem 8.4

Tags: geometry



Points $D, E, F$ are selected on sides $BC, CA, AB$ correspondingly of triangle $ABC$ with $\angle C = 90^\circ$ such that $\angle DAB = \angle CBE$ and $\angle BEC = \angle AEF$. Show that $DB = DF$. (Proposed by Mykhailo Shtandenko)