Circle Properties

A diameter goes from one point on the circumference to another through the centre. It contains two radii, so $d=2r$. For example, a circle with radius $4\text{ cm}$ has diameter $8\text{ cm}$. A chord also joins two points on the circumference, but it need not pass through the centre. Every diameter is a chord; not every chord is a diameter.

Curved parts and enclosed regions

An arc is a part of the circumference. You can draw one with a compass just as you draw a whole circle, but stop after part of a turn. A sector is the region enclosed by two radii and the arc between their ends: it resembles a slice of pizza. A segment is the region enclosed by a chord and an arc: unlike a sector, it does not need two radii as its straight boundaries. The same chord can bound a smaller and a larger segment on opposite sides.

A tangent is a straight line that touches the circle at exactly one point. A line cutting across the circle and meeting it at two points is not a tangent, even if only a short part of that line has been drawn. These names describe different things: an arc is curved boundary, a chord is a straight line segment, while a sector or segment is an area within the circle.

Drawing and describing circles

To draw a circle of a given radius, mark its centre, set a compass to that radius using a ruler, and turn the pencil through a full revolution. For an arc, turn it through only the required part of the revolution. If you are given the diameter instead, halve it to set the compass radius. A clockwise turn goes in the direction of a clock’s hands; anticlockwise is the opposite direction. Either direction gives the same circle, but it matters when an instruction specifies which way to draw an arc.