This article investigates the knowledge arising in mathematics teachers' planning of how to manage transitions within and beyond dynamic geometry environments in the topic of circle theorems. The notion of situated abstraction is used to elaborate the central TPACK construct within mathematics education and address previous criticisms of the framework, specifically to clarify the distinction between the central construct and the dyadic constructs. Four case-study teachers each participated in a semi-structured interview based upon a pre-configured GeoGebra file. The teachers were asked to demonstrate how they would use the GeoGebra file to introduce students to the circle theorem that the angle at the centre of the circle, subtended by an arc, is double the angle at the circumference subtended by the same arc. The visual and audio aspects of the GeoGebra interviews were recorded and the TPACK framework used to analyse teachers' knowledge arising in the four interviews. The central TPACK construct is illustrated with examples of teachers' strategies for capitalising on transitions within and beyond dynamic geometry environments for the purposes of teaching circle theorems and contrasted with the dyadic construct of TCK. The utility of the theoretical elaboration of the TPACK construct within mathematics education is demonstrated and implications discussed.