MathNet 2018-part-07 — 177 problems (EN–VI) Question 107

An isosceles right triangle $ABC$ has area $1$. Points $D$, $E$, $F$ are chosen on $BC$, $CA$, $AB$ respectively such that $DEF$ is also an isosceles right triangle. Find the smallest possible area of $DEF$.

Proposed by: Yuan Yao