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

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Explanation

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Copyright © 1996-2018 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.

This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at https://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.

What if applet does not run?

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 © 1996-2018 Alexander Bogomolny