Harmonic ratio

C and D divide AB harmonically since AC:CB = AD:DB. (Note that C divides AB internally, while D divides it externally.

The construction involves both Ceva's theorem and Menelaus' theorem. While the triangles, transversal etc can be seen in the diagram below (if you wish - use the check box), the combination of the theorems is left "as an exercise for the reader".

To download this Geogebra file click here.