## Circle Properties

A circle is a plane shape formed by a curve such that all points on the curve are the same distance from a fixed point, called the centre.

### Definitions

 A circumference is the distance around a circle. A radius is the distance from the centre to any point on the circumference. A diameter is a chord that passes through the centre.The length of the diameter is twice the length of the radius. An arc is a part of the circumference. A major arc is more than half of the circumferene. A minor arc is less than half of the circumference. A chord is a line joining two points on the circumference. A segment is an area of a circle bounded by a chord and the circumference. A sector is an area of a circle bounded by two radii and the circumference. A tangent is a line that touches the circumference of the circle at only one point. Concyclic points lie on the circumference of the same circle. e.g. A, B and C are concyclic points. Concentric circles have the same centre. e.g. The two circles shown are concentric. Two radii in a circle form part of an isosceles triangle. e.g. OAB is an isosceles triangle. A = B ### Tangents

 A tangent to a circle forms an angle of 90°with the radius at the point of contact. e.g. OAB = 90° Two tangents to a circle from a point are equal in length. A line from the point to the centre of the circle is an axis of symmetry. e.g. AB = AC m is an axis of symmetry. 