3. Angles Subtending the Same Arc
Chord CD cuts through our circle and breaks it into a major segment and a minor segment.
1. Turn on Centre Angle.
is the angle subtending the chord CD at Point O, the centre of the circle.
2. Turn on Circumference Angle 1.
is the angle subtending the chord CD at point B on the circumference.
What is the relationship between and ?
3. Turn off Circumference Angle 1. Turn on Circumference Angle 2.
is the angle subtending the chord CD at point A on the circumference.
What is the relationship between and ?
4. Turn off Center Angle. Turn on Circumference Angle 1.
and both subtend the same chord (or arc) from the same segment of a circle.
What is the relationship between and ?
EXTRA FUN
Move chord CD above the centre of the circle so that points A and B now lie in a minor segment.
Does the relationship between the angles change if points A and B lie in a minor or major segment?
Turn the chord off. Turn the centre angle on.
Move Point B below the centre of the circle so that a quadrilateral is formed.
Does this diagram provide insight into the relationship between opposite angles in a quadrilateral?