Four Circles In a Triangle: What Is It About? A Mathematical Droodle   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 http://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet. Buy this applet What if applet does not run? Explanation Copyright © 1996-2008 Alexander Bogomolny                         Four Circles In a Triangle The applet suggests the following theorem [Evelyn, pp. 39-42]: Assume in ABC 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 http://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet. Buy this applet 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. Copyright © 1996-2008 Alexander Bogomolny

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