n≥=3 lines lie in the same plane and are concurrent at point O.
If y = mx is the equation of a line passing through the origin O
(where m is the slope), then m_k labels the line y = tan(k*180°/n)*x
(for k = 0 to n-1). Note: If n is even and k = n/2, then line m_k is
perpendicular to line m₀. Point P (distinct from O) is an arbitrary point
in the plane of the n lines. F_i is the foot of the perpendicular from
point P to line m_i (for i = 0 to n-1).

Prove that F₀F₁...F_n-1 is a regular n-gon.
  

(In reply to Solution by Harry)

Posted by Bractals on 2017-07-10 07:25:50