Chord CD cuts through our circle and breaks it into a [url=https://www.geogebra.org/m/zhmjaatc][color=#0000ff]major segment[/color][/url] and a [color=#0000ff][url=https://www.geogebra.org/m/zhmjaatc]minor segment[/url][/color].[br][br][b][i]1.[/i][/b] [i][b]Turn on Centre Angle.[br][/b][/i][br][math]\angle COD[/math] is the angle subtending the chord CD at Point O, the centre of the circle.[br][br][i][b]2. Turn on Circumference Angle 1.[/b][/i][br][br][math]\angle CBD[/math] is the angle subtending the chord CD at point B on the circumference.[br][br]What is the relationship between[math]\angle CBD[/math] and [math]\angle COD[/math]?[br][br][b][i]3. Turn off Circumference Angle 1. Turn on Circumference Angle 2.[br][br][/i][/b][math]\angle CAD[/math] is the angle subtending the chord CD at point A on the circumference.[br][br]What is the relationship between[math]\angle CAD[/math] and [math]\angle COD[/math]?[br][br][i][b]4. Turn off Center Angle. Turn on Circumference Angle 1.[/b][br][br][math]\angle CAD[/math] [/i]and [math]\angle CBD[/math] both subtend the same chord (or arc) from the same segment of a circle.[br][br]What is the relationship between [i][math]\angle CAD[/math] [/i]and [math]\angle CBD[/math]?

Move chord CD above the centre of the circle so that points A and B now lie in a minor segment.[br][br][i]Does the relationship between the angles change if points A and B lie in a minor or major segment?[/i][br][br]Turn the chord off. Turn the centre angle on.[br][br]Move Point B below the centre of the circle so that a quadrilateral is formed.[br][br][i]Does this diagram provide insight into the relationship between opposite angles in a quadrilateral?[/i]