Circle Geometry

Circle geometry looks like a list of theorems to memorise. It is not. Every result in these five lessons is derived from something you already accept, and the derivations are short. Learn the three or four ideas that generate them and the list looks after itself.

5lessons

10syllabus points

3-4hstudy

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Lessons

The Language of Circles

Chord, arc, segment, sector and secant, and which arc an angle stands on

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Chord Properties

The perpendicular from the centre bisects a chord, and equal chords are equidistant

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Angle Properties

One theorem, the angle at the centre, and three corollaries that cost a line each

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Tangents and the Radius

One tangent per point, the perpendicular, equal tangents and the alternate segment

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Secants and Products

Chords, secants and the tangent case, all from one similar-triangle argument

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Focus Area Snapshot

5lessons

10syllabus points

15worked examples

40questions

Where this leads

This is a Path focus area, sitting outside the Core and preparing you for Mathematics Extension 1 in Year 11. The habit it builds matters more than the theorems: state what is given, name the reason for every line, and stop when the conclusion is reached.

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