The gear system of a bicycle involves a simple arrangement of a large sprocket wheel of radius 9.5cm and a small sprocket wheel of diameter 7cm, with a chain running between them. On one bicyycle the distance the chain travels between the sprocket wheels is 36cm.
a) What is the distance between the centres of the two sprocket wheels?
b) What is the clearence (minimum distance) between the two sprocket wheels?
c) What is the minimum length of chain needed to go around the whole system?
Hint: draw the two wheels (circles), one line tangent to both circles at $A$ and $B$ (part of this represents the chain) and two radii joining centers $P$ and $Q$ to their tangency points $A$ and $B$. You have then a right trapezoid $ABQP$, of which you know the length of two bases (radii of circles) and the height (36 cm). It is not difficult then to compute (with the help of Pythagoras' theorem) the length of the fourth side, which is the distance between centers.