Posts tagged 'h-e-huntley'

GC-04.01 — H. E. Huntley's Golden Ratio in the 3-4-5 Right Triangle (1970) cOC: x**2 + (y - 3/2)**2 - 9/4 = 0 BO: -3*x/2 - 3*y + 9/2 = 0 Golden major PQ = 3 Golden minor BP = -3/2 + 3*sqrt(5)/2 A = (0, 4) O = (0, 3/2) T = (6/5, 12/5) C = (0, 0) B = (3, 0) P = (3*sqrt(5)/5, 3/2 - 3*sqrt(5)/10) Q = (-3*sqrt(5)/5, 3*sqrt(5)/10 + 3/2) A O T C B P Q

GC-04.01 · H. E. Huntley’s Golden Ratio in the 3-4-5 Right Triangle (1970)

In a \(3\text{-}4\text{-}5\) right triangle ABC (\(|BC|=3, |AC|=4, |AB|=5\)), let the internal bisector of \(\angle ABC\) meet leg AC at O. Circle cOC centered at O through C intersects line BO at P and Q such that \(|PQ|/|BP| = |BQ|/|PQ| = \phi\).