Manifesto | Index | What's new | rss feed

| Bookmark |

| Follow us

| Recommend | Contact |

Vecten's Theorem

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?

Following is a listing of a few properties of Vecten's configuration:

Lines AA_b and BB_a meet on the C-altitude of ΔABC.
Lines AA_b and CC_b are perpendicular and equal. (This follows from the congruence of triangles ABA_b and C_bBC.) Assume AA_b and CC_b meet at point S_b and introduce similarly S_a and S_c.
Line A_cC_a passes through S_b and bisects a pair of angles at that point. (Quadrilateral AC_aC_bS_b is cyclic as having opposite angles at C_a and S_b both 90°. In the circumcircle, angles AS_bC_a and AC_bC_a, the latter being 45°, are subtended by the same chord AC_a. Hence angle AS_bC_a is also 45°.)
Lines AS_a, BS_b, and CS_c are concurrent and each passes through the center of one of Vecten's squares.
Let T_a, T_b, and T_c denote the centers of Vecten's squares BCA_cA_b, etc. Then AT_a is equal and perpendicular to T_bT_c.
A_cB_c² + B_aC_a² + A_bC_b² = 3(AB² + BC² + AC²).

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

Copyright © 1996-2007 Alexander Bogomolny

40617852

Supported by