### Four Circles In a Triangle: What Is It About?

A Mathematical Droodle

What if applet does not run? |

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Copyright © 1996-2017 Alexander Bogomolny

### Four Circles In a Triangle

The applet suggests the following theorem [Evelyn, pp. 39-42]:

Assume in ΔABC three circles are drawn that touch externally the incircle and internally three pairs of the adjacent sides of the triangle. The three lines that connect the opposite points of tangency (as in the applet below) concur in a point. |

What if applet does not run? |

The theorem is a particular case of a more general Seven Circles Theorem.

### References

- Evelyn, C. J. A., Money-Coutts, G. B., Tyrrell, J. A.,
__A Theorem about a Triangle and Six Circles__, in*The Seven Circles Theorem and Other New Theorems*, Stacey International, 1974.

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