Circle geometry

Background knowledge	Description
It all starts with a line	Seeing how the properties of a straight line lead to the the special characteristics of angles in parallel lines.
Properties of parallelograms	Discovering properties of parallelograms that relate to their angles, their sides and their diagonals.
Special triangles	Explanations of right angle triangles, isosceles triangles and equilateral triangles.

Circle geometry	Description
Vocabulary of circles	An explanation of words used when talking about circles. Centre, circumference, points on the circle, radius, diameter, chord, arc, segment, sector, secant, tangent, cyclic quadrilateral.
Angle at centre and angle at circumference	An important property of circles is that the size of the angle subtended at the centre is twice the size of the angle subtended at the circumference. “Subtended” is explained, as well as how this property comes about.
Consequences of relationship between angles at centre and circumference	The consequences of the relationship between the angles at the centre and circumference are explained. 1) Angles in the same segment are equal. 2) Angles on the diameter are equal to 90 degrees. 3) Opposite angles of cyclic quadrilaterals add up to 180 degrees. 4) The external angle of a cyclic quadrilateral is equal to the interior opposite angle.
Tangents to a circle.	Special features of tangents are explained. 1) The angle between a tangent and a radius (and diameter) is equal to 90 degrees. 2) The angle between a tangent and a chord is equal to the angle at the circumference. 3) Two tangents to a circle from the same point are equal in length.
Area of a circle	Explains the relationships between the circumference, diameter and radius of a circle and how the relationships lead to the formula for the area of a circle.

GeoGebra interactive tools	Description
Circle geometry	For experimenting with material presented in the recorded lessons.