Circle Geometry

Circle Geometry forms an important part of your Mathematics A iGCSE syllabus. Here, let’s walk through key points, in line with the Geometry and Measures unit.

Definition: A circle is a twodimensional shape made by drawing a curve that is always the same distance from a central point.

Diameter: This is a straight line passing through the centre of a circle, connecting two points on the boundary.

Radius: The radius of a circle is any straight line from its centre to its boundary. The radius is always half the length of the diameter.

Circumference: This is the term for the perimeter of a circle. It is calculated by using the formula C = πd or C = 2πr, with ‘d’ standing for diameter and ‘r’ for radius.

Arc: Part of a circle’s circumference is called an arc.

Sector: A section of a circle, bounded by two radii and their intercepted arc, is referred to as a sector.

Segment: A portion of a circle, bounded by a chord and the associated arc, is known as a segment.

Tangent: This is a straight line that touches the circle at a single point without cutting across it.

Chord: Any straight line segment joining two points on a circle’s boundary, but not passing through the centre, is called a chord.

Pi (π): This mathematical constant is the ratio of a circle’s circumference to its diameter. The value of Pi is approximately 3.14159.

A full circle is 360 degrees. This means that the angle subtended at the centre of the circle by the circumference is 360°.

If two radii are drawn to the endpoints of an arc (or a chord), they subtend an angle to that arc (or chord). The size of this angle varies depending on the position of the radii.

Supplementary angles can be formed by chords, tangents, and secants interacting with circles.

Important concepts include the Alternate Segment Theorem, Angles in the Same Segment, Angle at the Centre and Inscribed Angles. Review definitions, properties and problemsolving strategies related to these.

Practice solving problems. These can include but are not limited to: finding the measurements of angles or lengths in circle theorems such as tangentradius, angle on diameter is a right angle, angles in the same segment, and cyclic quadrilateral etc.
Remember, understanding the definitions and properties is key, but so is applying this knowledge. So make sure to practise with a wide variety of problems.