Posts tagged 'cyclic-quadrilateral'

F.15 Cyclic Quadrilateral

A cyclic quadrilateral WXYZ whose interior angles form the arithmetic progression theta, 2*theta, 3*theta, 4*theta has theta = 36 degrees (W = 36, X = 72, Y = 144, Z = 108) and golden-ratio diagonals |XZ| = 2 sin(36) = sqrt(3 - phi) and |WY| = 2 sin(72) = phi*sqrt(3 - phi) in the unit circle; by contrast, no non-trivial cyclic quadrilateral can have interior angles in geometric progression theta, k*theta, k^2*theta, k^3*theta.