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Find the perimeter of KTL

Source: XVII Sharygin Correspondence Round P1

March 2, 2021
geometryperimeter

Problem Statement

Let ABCABC be a triangle with ∠C=90∘\angle C=90^\circ. A line joining the midpoint of its altitude CHCH and the vertex AA meets CBCB at point KK. Let LL be the midpoint of BCBC ,and TT be a point of segment ABAB such that ∠ATK=∠LTB\angle ATK=\angle LTB. It is known that BC=1BC=1. Find the perimeter of triangle KTLKTL.
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