Three Tangent Circles
- Judah L Schwartz
Three circles, each of which is tangent to the other two have their centers on a line. You can explore this problem by moving the WHITE dot. What is the relationship between the circumference of the yellow region and the combined circumferences of the two interior circles? How long is the vertical tangent to the two interior circles? What is the area of the yellow region? **** Do you regard this applet as the basis for a student task in algebra? geometry? both? neither? Would you give this task to middle school students? Why or why not?
adapted from Polya - Mathematical Discovery
For some very beautiful variations on this problem - look up "Arbelos" or "The Shoemaker's Knife"