Let L be the circle in the x-y plane with center the origin and radius 38. Let S be a moveable circle with radius 8 . S is rolled along the inside of L without slipping while L remains fixed. A point P is marked on S before S is rolled and the path of P is studied. The initial position of P is (38,0). The initial position of the center of S is (14,0) . After S has moved counterclockwise about the origin through an angle t the position of P is:

x = 14cost + 24cos(7/12t)
y= 14sint - 24sin (7/12t)

Required:
How far does P move before it returns to its initial position?