Let L be the circle in the x-y plane with center the origin and radius 76.
Let S be a moveable circle with radius 68 . 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 (76,0).
The initial position of the center of S is (8,0) .
After S has moved counterclockwise about the origin through an angle t the position of P is x=8cost+68cos(2/17 t)
y=8sint-68sin(2/17 t)
How far does P move before it returns to its initial position?
Hint: You may use the formulas for cos( u+v) and sin( w /2).
S makes several complete revolutions about the origin before P returns to (76,0). This is all the information and it is enough to solve the problem.