Posts tagged 'jingcheng-tong'

GC-07.03 — Jingcheng Tong's Area-Bisecting Chord in a 1:3 Trapezoid AB: 2*x - 2*y + 6 = 0 DC: 2*x + 2*y - 6 = 0 MN: y - 3 + sqrt(5) = 0 Golden major AM = -sqrt(2) + sqrt(10) Golden minor MB = -sqrt(10) + 3*sqrt(2) D = (1, 2) C = (3, 0) N = (sqrt(5), 3 - sqrt(5)) A = (-1, 2) B = (-3, 0) M = (-sqrt(5), 3 - sqrt(5)) D C N A B M

GC-07.03 · Jingcheng Tong’s Area-Bisecting Chord in a 1:3 Trapezoid

Let ABCD be a trapezoid with parallel bases AD and BC satisfying \(|BC| = 3|AD|\). The chord MN parallel to the bases that bisects the area of ABCD divides both non-parallel legs AB and DC in the golden ratio: \(|AM|/|MB| = |DN|/|NC| = \phi\).