Pierre Botha.NIS

 Learners can  :

• Student will know the definition of circular sector and circular segment. 
• continue to use the skills of developing geometric proof from postulates, theorems, conclusions, properties and features;
  
• know and recognize the language associated with circle properties: segments (lines) and angles in circle (chord, tangent, secant, central and inscribed angles) 
  
• prove and apply the chord properties in the circle, such as * alternate segment theorem, * intersecting chord theorem, * perpendicular bisector of a chord passes through the center of a circle * two chords of the same circle are equal if and only if their perpendicular bisectors are equal * a chord AB of a circle is larger than a chord CD of the same circle if and only if the perpendicular bisector of AB, OE, is smaller than the perpendicular bisector of CD, OF. So AB > CD 〈=〉 ⇔ OE < OF
• investigate the geometry of an arrangement of a line and a circle, two circles; 
  
• understand the terms associated with circumcircle and incircle of a triangle;
  
• understand the concept of inscribed and circumscribed polygons; 
  
• identify the location of centers of circumscribed and inscribed circles in polygons;
  
• prove and apply properties and characteristics of circumscribed and inscribed quadrilaterals: e.g. opposite angles in a quadrilateral inscribed in a circle add up to 180°, the sum of the lengths of opposite sides of a quadrilateral circumscribed around a circle are equal 
  
• prove and apply the two tangent theorem (the lengths of two tangents drawn from the same point are equal); 
•  prove and apply the theorems that * an inscribed angle is half the central angle; * the angle inscribed in a semi-circle is 90°; * angles in the same segment are equal