Problem

Source: IGO 2024 Elementary Level - Problem 3

Tags: geometry



Inside a convex quadrilateral $ABCD$ with $BC>AD$, a point $T$ is chosen. $S$ lies on the segment $AT$ such that $DT = BC, \angle TSD = 90^\circ$. Prove that if $\angle DTA + \angle TAB + \angle ABC = 180^\circ$, then $AB + ST \geqslant CD + AS$. Proposed by Alexander Tereshin - Russia