MathNet 2022-part-03 — 197 problems (EN–VI) Question 73

In isosceles right triangle $ABC$ with $\angle BAC = 90^\circ$ and $AB = AC = 7$, let $D$, $E$ and $F$ be points on sides $BC$, $CA$ and $AB$ respectively. Given that $\angle EDF = 90^\circ$, $DE = 5$, $DF = 3$, find the length of $BD$.