## Iterations on a Circle Through Three Points

Prof. W. McWorter passed me on the following problem:

Consider a circle c and three points P, Q, and R inside c. For any point X on c, do the following. Extend the line XP to meet c at X. Extend the line _{P}X_{P}Q to meet c at X. Finally, extend the line _{Q}X to meet _{Q}Rc at X. Define _{R}f(X) = X._{R}f^{ n}(X) converge to a point X' on c such that f(X') = X'? |

The applet below helps to experiment with the problem. (The problem remains meaningful even if some or all of the points *P*, *Q*, *R* lie outside the circle.)

What if applet does not run? |

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