SHARYGIN 2021 Problem 1

Let $ABC$ be a triangle with $\angle C=90^\circ$ . A line joining the midpoint of its altitude $CH$ and the vertex $A$ meets $CB$ at point $K$ . Let $L$ be the midpoint of $BC$ ,and $T$ be a point of segment $AB$ such that $\angle ATK=\angle LTB$ . It is known that $BC=1$ . Find the perimeter of triangle $KTL$ .