# 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:

$\frac{AB}{AC} = \frac{BD}{CD}.$

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

### Angle Bisector

• Angle Bisector
• Angle Bisector Theorem
• 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