"Consider ∆OAH AH - a sin Θ-a/3
The circumference of base circle H is 2∏ ⋅ a/3 - 2/3 a∏
The lateral surface of the cone can be cut through by the straight line OA and laid flat as a cone net which is pictured in the diagram to the right. It takes the form of a sector of a circle with center focus O and radius OA = a
The central angle ∝ of the lateral surface is ∝ = (2/3 a∏)/(2 a∏) x 360° - 120
The minimum distance traveled by the by the [sic] moving point P is when it travels along line segment AA¹ as shown on the flat cone net diagram."