MA5.317MG
Applies deductive reasoning to prove circle theorems and to solve related problems
Outcomes

Prove and apply angle and chord properties of circles (ACMMG272)

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

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

Apply chord and angle properties of circles to find unknown angles and lengths in diagrams
Examples

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