In the figure below, the three points
of intersection of the adjacent angle trisectors of any triangle
ABC form an equilateral triangle DEF called Morley's triangle.
Morley center is the intersection of AF, BE, and CD.

Apollonius for iPad: Morley's Theorem
I drew the geometric construction above using Apollonius for iPad.
Apollonius is an interactive geometry app (IGS, or Dynamic Geometry
Environment, DGE). It allows you to create geometric constructions, such as those that can be made using a ruler and a compass, and subsequently move parts of your constructions to explore the relationship between the geometric objects on the screen.
Apollonius is inspired by software such as GeoGebra, The Geometer's Sketchpad and Cabri,
but its interface is especially designed for touch screen.
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