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 m

_{0}. 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 F

_{0}F

_{1}...F

_{n-1}is a regular n-gon.