MA5.3-17MG
Applies deductive reasoning to prove circle theorems and to solve related problems
Outcomes
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Prove and apply angle and chord properties of circles (ACMMG272)
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prove the following chord properties of circles: CCT
chords of equal length in a circle subtend equal angles at the centre and are equidistant from the centre
the perpendicular from the centre of a circle to a chord bisects the chord; con
Examples
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prove the following angle properties of circles: CCT
the angle at the centre of a circle is twice the angle at the circumference standing on the same arc
the angle in a semicircle is a right angle
angles at the circumference, standi
Examples
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Apply chord and angle properties of circles to find unknown angles and lengths in diagrams
Examples
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prove the following chord properties of circles: CCT
chords of equal length in a circle subtend equal angles at the centre and are equidistant from the centre
the perpendicular from the centre of a circle to a chord bisects the chord; con
- Prove and apply tangent and secant properties of circles