MathDB
ratio of areas wanted, right triangle and 2 symmetric points related

Source: Czech-Polish-Slovak Junior Match 2018, Team p2 CPSJ

March 7, 2020
ratioareasgeometrysymmetryright triangle

Problem Statement

Given a right triangle ABCABC with the hypotenuse ABAB. Let KK be any interior point of triangle ABCABC and points L,ML, M are symmetric of point KK wrt lines BC,ACBC, AC respectively. Specify all possible values for SABLM/SABCS_{ABLM} / S_{ABC}, where SXY...ZS_{XY ... Z} indicates the area of the polygon XY...ZXY...Z .