Year 10/11 maths revision: terms for a circle: centre, radius, chord, diameter, circumference, tangent, arc, sector, segment and subtended.
For a high grade you need to know the proofs for the circle theorems.
The 'radius' of a circle is the distance from the centre to its edge.
The 'diameter' of a circle is the distance between one edge of a circle, through its centre, to the edge on the other side.
The diameter of a circle is twice the value of its radius.
The 'circumference' is the distance around the edge of a circle. The circumference of a circle can be calculated by the formula: 2πr or πD
The 'area' of a circle can be calculated by the formula: πr²
The 'tangent' to a circle is a line which touches a circle at one point; without cutting across the circle.
An 'arc' is part of the circumference of a circle.
A 'chord' a line which goes from one point to another on the circle's circumference.
A 'sector' is a pie-slice portion of a circle, e.g. a semicircle because it is a half of the whole circle.
A 'segment' is the portion of a circle between a chord of a circle and its associated arc.
The angle x is an angle 'subtended' by the arc.
Prove that the angle subtended by an arc at the centre (2b) is twice the angle subtended at the circumference (b).
Hint: Draw a line from the centre o, to the point where the two lines cross the circumference at the top of the diagram
This makes two isosceles triangles with sides equal to the radius.