A Circle Crosses A Triangle: What is it about?
A Mathematical Droodle


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Explanation

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Copyright © 1996-2017 Alexander Bogomolny

Explanation


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?

From a point P in the plane of ΔABC drop perpendiculars to the side lines of the triangle. Pass a circle through the feet of the three perpendiculars. In general, the circle will cross the side lines at another three points. At those points erect perpendiculars to the side lines. The latter three lines always concur at a point.

The proof is simple. The point of concurrence is the symmetric image of P in the center of the circle.

References

  1. R. Honsberger, More Mathematical Morsels, MAA, 1991

|Activities| |Contact| |Front page| |Contents| |Geometry|

Copyright © 1996-2017 Alexander Bogomolny

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