Posts tagged 'h-s-m-coxeter'

GC-02.01 — George Odom's Equilateral Midline & Circumcircle Chord (1983) cO: x**2 + y**2 - 4 = 0 LM: y - 1/2 = 0 Golden major LM = sqrt(3) Golden minor MY = (-sqrt(3) + sqrt(15))/2 O = (0, 0) X = (-sqrt(15)/2, 1/2) A = (0, 2) B = (-sqrt(3), -1) C = (sqrt(3), -1) L = (-sqrt(3)/2, 1/2) M = (sqrt(3)/2, 1/2) Y = (sqrt(15)/2, 1/2) O X A B C L M Y

GC-02.01 · George Odom’s Equilateral Midline & Circumcircle Chord (1983)

Let ABC be an equilateral triangle inscribed in circle cO, and let L and M be the midpoints of sides AB and AC. Extending midline LM to meet circumcircle cO at X and Y divides the chord in the golden ratio: \(|LM|/|MY| = |LY|/|LM| = \phi\).