**11.1- Introduction**

**Circle Definitions**

This section of Revision Maths defines many terms in relation to circles, including: Circumference, Diameter, Radius, Chord, Segment, Tangent, Point of contact, Arc, Angles on major and minor arcs, Angle of Centre and Sectors.

**Circumference:** The circumference of a circle is the distance around it.

**Diameter:** Any straight line that passes through the centre of the circle to two points on the perimeter.

**Radius:** Any straight line that originates at the centre of a circle and ends at the perimeter.

**Chord:** A straight line whose ends are on the perimeter of a circle. A diameter is the longest chord possible.

**Segment:** A part of the circle separated from the rest of a circle by a chord.

**Tangent:** A tangent to a circle is a straight line which touches the circle at only one point (so it does not cross the circle – it just touches it).

**Point of contact:** Where a tangent touches a circle.

Arc: A part of the curve along the perimeter of a circle.

Angle on major arc: The larger of 2 angles when a circle is split into 2 uneven parts. Greater than 180 degrees.

**Angle of centre:** An angle at the centre of a triangle between two lines that intersect with the perimeter.

Angle at circumference on minor arc: The smaller of 2 angles when a circle is split into 2 uneven parts. Less than 180 degrees.

**Sector:** A portion of a circle resembling a ‘slice of pizza’.

**11.2- Circles 1**

This section explains circle theorem, including tangents, sectors, angles and proofs.

**11.3- Circles 2**

**11.4- Circle theorems**

Two Radii and a chord make an isosceles triangle.

The perpendicular from the centre of a circle to a chord will always bisect the chord (split it into two equal lengths).

Angles formed from two points on the circumference are equal to other angles, in the same arc, formed from those two points.

Angles formed by drawing lines from the ends of the diameter of a circle to its circumference form a right angle.

A tangent to a circle is a straight line which touches the circle at only one point (so it does not cross the circle- it just touches it).

A tangent to a circle forms a right angle with the circle’s radius, at the point of contact of the tangent.

The angle formed at the centre of the circle by lines originating from two points on the circle’s circumference is double the angle formed on the circumference of the circle by lines originating from the same points.

A cyclic quadrilateral is a four-sided figure in a circle, with each vertex (corner) of the quadrilateral touching the circumference of the circle. The opposite angles of such a quadrilateral add up to 180 degrees.

**11.5- Constructions and Loci**

Use the following loci and the method of intersecting loci for sets

of points in two dimensions which are:

(a) at a given distance from a given point

(b) at a given distance from a given straight line

(c) equidistant from two given points

(d) equidistant from two given intersecting straight lines

**11.6- Summary and Review**

**11.7- Assessment 11**

Question 1 : Calculate the area of the sector and arc length for a circle of radius r and the angle subtended at the center is θ° ?

Question 2 : Are those 2 triangles congruent, Why?