Circle Geometry

Understanding Circles

Understand that a circle is a collection of all points in a plane that are a fixed distance from a centre point.
Be familiar with the different parts of a circle: radius, diameter, circumference, and arc.
Realise that the radius connects the centre of the circle with any point on the circle itself.
Know that the diameter is a line that cuts the circle into two equal halves, passing through the centre. It is twice the length of the radius.
Understand that the circumference is the total length of the edge of the circle.
Recognise an arc as a portion of the circumference of the circle.

Understand the Central Angle Theorem: The measure of the angle at the centre of the circle is twice that of the angle on the circumference when they both span the same arc.
Understand the Alternate Segment Theorem: The angle between a tangent and a chord through a point of contact is equal to the angle in the alternate segment.
Understand the Chord Properties: Equal length chords from the same circle or congruent circles intercept congruent arcs and subtend angles of the same measure.
Know the Tangent Properties: Tangents from the same external point are equal in length, and the angles they form with the line joining the centre of the circle to the point are equal.

Understand that the inscribed angles encompassing an arc are all equal.
Know that the angle in a semi-circle is a right angle.
Understand the concept of segments in a circle, created by drawing a chord. Familiarise yourself with the terms “major segment” and “minor segment”.
Recall Cyclic quadrilaterals: In any quadrilateral inscribed in a circle, the opposite angles add up to 180 degrees.

Identify circles within 3D shapes, such as cylinders and spheres.
Understand how to calculate the surface area and volume of these 3D shapes using relevant formulae involving circles.
Understand the concept of a great circle on a sphere and how it is analogous to a line in two dimensions.