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Circle geometry (or circle theorems) involves looking at angle properties when lines and shapes are drawn in circles. Once you can identify and label parts of a circle, it is possible to add lines, triangles and quadrilaterals inside a circle. Circle theorems can help find missing angles.
You should be able to label parts of a circle.
| NAME | DESCRIPTION | ILLUSTRATION |
| Radius | A line from the centre to the edge of the circle. |  |
| Diameter | A line across the circle, going through the centre. |  |
| Circumference | The perimeter of the circle. |  |
| Arc | A section of the circumference. |  |
| Chord | A line segment joining two points on the circumference. |  |
| Sector | Part of a circle bound by an arc and two radii. |  |
| Segment | Part of a circle bound by a chord and an arc. |  |
There are eight circle theorems that you should learn.
| THEOREM | DESCRIPTION | ILLUSTRATION |
| Angles in the same segment are equal. | | |
| The angle at the centre is twice the angle at the circumference. | | |
| The angle in a semicircle is . | | |
| The radius and tangent are perpendicular. | | |
| The perpendicular bisector of a chord goes through the centre. | | |
| Opposite angles in a cyclic quadrilateral add up to . | | |
| Two tangents from the same point are the same length. | | |
| The alternate segment theorem. | The angle at the tangent is equal to the angle in the alternate segment. | |
In the circle shown, . Find , and .
is twice the angle at the circumference .
as it is the angle in a semicircle. Therefore and add up to .
is a straight line, so can be found.
The alternate segment theorum states that the angle at the tangent is the same as the angle in the alternate segment.
An arc is a section of the circumference.
A cyclic quadrilateral is a quadrilateral that is inside a circle, where the vertices of the quadrilateral touch the circumference of the circle. Opposite angles in a cyclic quadrilateral add up to 180 degrees.
Beta
