Properties of Circles

The main parts are the centre, the radius, the diameter, a chord, an arc, a segment, a sector and a tangent. The one property every circle has is that each point on its edge is the same distance from the centre; that distance is the radius, which is why a wheel rolls smoothly. The diameter, through the centre, is twice the radius.

A chord is a straight line with both ends on the circle. The diameter is the special chord through the centre, and it is the longest chord you can draw; every other chord is shorter. A chord cuts off a segment, the area between the chord and the arc above it. In a circle with a radius of 7 cm, the longest chord is 14 cm.

The radius is the distance from the centre to any point on the edge, the same all the way round. The diameter is a line through the centre joining two points on the edge, so it is twice the radius. Double the radius to get the diameter and halve the diameter to get the radius: a 16 cm diameter means an 8 cm radius.

A sector is the slice-of-pie shape between two radii and the arc joining them, so it always reaches the centre. A segment is the area between a chord and the arc above it, so its straight side is a chord and it does not reach the centre. The arc is the part of the circle’s edge that each one uses.

A tangent is a straight line that touches the circle at exactly one point. At that point it is always perpendicular to the radius, meaning the tangent and the radius meet at a right angle of 90°. This is true for every tangent, whichever point on the edge it touches, and it is the fact that circle theorem questions use most.

Draw a circle around each place with the right radius. For the points 5 cm from A and 3 cm from B, set a compass to 5 cm and draw a circle centred on A, then 3 cm centred on B. Where the circles cross are the points that fit both. The same method places a car park a set distance from two shopping centres.