A Property of Angle Bisectors III

The applet below illustrates a proof of the Angle Bisector theorem suggested by Gregoire Nicollier, Sion, Switzerland. The proof is a modfication of the one submitted by Professor McWorter and applies to both internal and external angle bisectors:

12 January 2015, Created with GeoGebra

\(\frac{AB}{AC} = \frac{BD}{CD}.\)

I leave it as a proof without words. It's a good exercise to figure out what is it about.

Related material
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Angle Bisector

  • Angle Bisector
  • Angle Bisector Theorem
  • All about angle bisectors
  • Angle Bisectors in Ellipse
  • Angle Bisectors in Ellipse II
  • Angle Bisector in Equilateral Trapezoid
  • Angle Bisector in Rectangle
  • Property of Angle Bisectors
  • Property of Angle Bisectors II
  • External Angle Bisectors
  • Projections on Internal and External Angle Bisectors
  • Angle Bisectors On Circumcircle
  • Angle Bisectors in a Quadrilateral - Cyclic and Otherwise
  • Problem: Angle Bisectors in a Quadrilateral
  • Triangle From Angle Bisectors
  • Property of Internal Angle Bisector - Hubert Shutrick's PWW
  • Angle Bisectors Cross Circumcircle
  • For Equality Choose Angle Bisector
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