The Greek mathematician Apollonius (c. 200 BC) proved that for any three circles with no common points or common interiors, there are eight ways to draw a circle that is tangent to the three given circles.[br][br]Shown are two examples. Notice that the colored circles have not moved, but that the "clear" circle has been moved so that it is tangent to all three colored circles.[br][img width=161px;,height=125px;]https://lh6.googleusercontent.com/pSwGJbJoUn062uwrBhccB8gi8nM6zxHOF-A5w1wHSMB7cocB2VefI7S__FD6yh3ULe4BmRiA3hknAio6V0Bh0_IwqcVVTrD6e7SiaoE-m8NE0F3obI9AEsu8avWuepxEntfH6RFrje0[/img] [img width=170px;,height=132px;]https://lh4.googleusercontent.com/g-Tw3ZuIloO-JuJxw1MDcY4kJaMUx2nYLnpX5a6_s4rZYjIVofkmonbzIRpLGhSFI3xxhHRrXgR4mXjl4clUCiZkEh-abc_6DaC5Hc4pbQ_vwqpT2WFo8BvqkkMqDMcgkL3qSP-zMZA[/img][br]In each of the diagrams below, your job is to move the "clear" circle so that it is tangent to the three colored circles. You need to do this in 8 unique ways, which is why there are 8 diagrams to complete.