Problem

Source: Czech-Polish-Slovak Junior Match 2017, individual p4 CPSJ

Tags: geometry, perimeter, min, right triangle



Given is a right triangle $ABC$ with perimeter $2$, with $\angle B=90^o$ . Point $S$ is the center of the excircle to the side $AB$ of the triangle and $H$ is the intersection of the heights of the triangle $ABS$ . Determine the smallest possible length of the segment $HS $.