Four Circles In a Triangle: What Is It About?
A Mathematical Droodle

Explanation

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Copyright © 1996-2012 Alexander Bogomolny

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.

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

References

1. 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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Copyright © 1996-2012 Alexander Bogomolny