MathDB

2

Part of 2018 Czech-Polish-Slovak Junior Match

Problems(2)

hexagon, 2 // sides, diagonal divides into quadrilaterals equal perimeters

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

2/1/2020
A convex hexagon ABCDEFABCDEF is given whose sides ABAB and DEDE are parallel. Each of the diagonals AD,BE,CFAD, BE, CF divides this hexagon into two quadrilaterals of equal perimeters. Show that these three diagonals intersect at one point.
hecagonparalleldiagonalgeometryperimeter
ratio of areas wanted, right triangle and 2 symmetric points related

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

3/7/2020
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 .
ratioareasgeometrysymmetryright triangle