MathNet 2016-part-06 — 184 problems (EN–VI) Question 167

The points $A_1$ and $C_1$ are chosen on the sides $BC$ and $AB$ of the triangle $ABC$ so that the segments $AA_1$ and $CC_1$ are equal and perpendicular. Prove that if $\angle ABC = 45^\circ$, then $AC = AA_1$.

(Andrei Gogolev)