This topic primarily consists of demonstrating and utilising a range of circle properties related to chords, angles, tangents and secants. The study of circle geometry provides students an opportunity to develop their deductive reasoning, a critical skill required for testing hypotheses in mathematics and science, as well as solving everyday problems at home or at the workplace.
Students also further develop their ability to follow mathematical procedures in order to carefully construct diagrams, using compass-and-straight-edge or dynamic geometry software. Developing a general understanding of circle geometry provides students a foundation to explore how circles are applied by scientists in physical models, e.g. the orbit of planets, the motion of cars moving around a bend; as well as its prevalence in the world in 3-dimensional engineering constructions and everyday objects.
A student:
Students:
Prove and apply angle and chord properties of circles (ACMMG272)
Prove and apply tangent and secant properties of circles
Images created in GeoGebra Geometry
Link to: GeoGebra Diagrams
Playlist to GeoGebra Geometry tutorial (created by GeoGebra): https://www.youtube.com/playlist?list=PLITakOESY-2zqgJ4TWGNrqAPrsqolvxJf