Circle Geometry 1

CONTENT

A. Lines and regions of a circle.

B. Circle theorems including:

• Angles subtended by chords in circle;
• Angles subtended by chords at the centre;
• Perpendicular bisectors of chords;
• Angles in alternate segments.
• Cyclic quadrilaterals

ANGLES SUBTENDED BY CHORDS IN CIRCLE

The word chord is a straight line joining any two points such as A and B on the circumference of a circle. The chord divides the circle into two parts called the segments (minor and major)

The larger part of the circle is called the major segment while the smaller part – the minor segment. Each of these parts is called the alternate segment of the other.

Note: A major segment has a major arc while a minor segment a minor arc.

A circle is the set of all points at a constant distance from a fixed point in a plane. The fixed point is the centre of the circle, the distance from the fixed point (is constant), is called the radius.

It will be noted that it is the chord that subtends (projects out) angles viz:

From the diagram, P,Q and R are points on the circumference of a circle.