La Hire's Theorem: What Is It About?
A Mathematical Droodle
What if applet does not run? 
Activities Contact Front page Contents Geometry Eye opener
Copyright © 19962018 Alexander Bogomolny
La Hire's Theorem
The applet suggests the following theorem:
Let there be two points A and B outside the circle O. From points A and B draw tangents AC, AD, BE, BF to the circle. Then if B lies on CD, then A lies on EF. 
What if applet does not run? 
The theorem is a particular case of a more general La Hire's theorem:
If point A lies on the polar of point B, then point B lies on the polar of A. 
Indeed, for a point P outside the circle of reference, the polar passes through the tangency points of the tangents drawn from P to the circle.
References
 D. Wells, Curious and Interesting Geometry, Penguin Books, 1991
Poles and Polars

[an error occurred while processing this directive]
Activities Contact Front page Contents Geometry Eye opener
Copyright © 19962018 Alexander Bogomolny