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Czech-Polish-Slovak Junior geometry - excircle related

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

February 20, 2020
geometryperimeterminright triangle

Problem Statement

Given is a right triangle ABCABC with perimeter 22, with ∠B=90o\angle B=90^o . Point SS is the center of the excircle to the side ABAB of the triangle and HH is the intersection of the heights of the triangle ABSABS . Determine the smallest possible length of the segment HSHS .
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