Copy of Circle theorems

Circle Theorem 1: Angle at the Centre

[justify][b]1) [/b]The [color=#0000ff]central angle A [/color]and the [color=#0000ff]inscribed angle E[/color] are related to the[color=#76a5af] [/color][color=#93c47d]green arc CBD.[/color][color=#00ff00] [/color]Move the points C, D, and E to explore the model and then answer the questions below.[/justify][b] a) [/b]Write down what you notice about the relationship between the two angles.[br][br][b] b) [/b] Conjecture (idea for what the rule might be):[br][br][b] c)[/b] Justification (using rules you already know):

Circle Theorem 2: Angles in a semicircle

[justify][b]2) [/b]The [color=#ff00ff]diameter CD[/color] divides the[color=#0000ff] circumference into two equal parts (semicircles).[/color] The [color=#ff7700]inscribed angle E[/color] is subtended (related) by the [color=#38761d]green arc CBD[/color][color=#ff0000].[/color] Move point E around the circumference and then move the diameter BD as well. Explore and answer the questions below.[/justify][b] a) [/b]Write down what you notice?[br][br][b] b) [/b]Conjecture (idea for what the rule might be):[br][br][b] c)[/b] Justification (using rules you already know):

Circle Theorem 3: Inscribed angles subtended by the same arc

[b]3) [/b]The[color=#0000ff] inscribed angles [/color][color=#9900ff][b]B [/b][/color]and [color=#38761d][b]D[/b][/color] are subtended by the same [color=#ff00ff]pink arc AEC[/color]. Move the points around the circumference and then answer the questions below.[br][b][br] a)[/b] What do you notice?[br][br][b] b) [/b]Conjecture (idea for what the rule might be):[br][br][b] c) [/b]Justification (using rules you already know):

Circle Theorem 4: Cyclic quadrilateral

[b]4) [/b]The [color=#9900ff]quadrilateral ABCD[/color] is inscribed in the circle. Move the points around the circle and answer the questions below.[b][br][br] a) [/b]What do you notice?[br][br][b] b) [/b]Conjecture (idea for what the rule might be):[br][br][b] c) [/b]Justification (using rules you already know):

Circle Theorem 5: Tangent on a Circle (Tangent and Radius)

[b]6) [/b]The [color=#9900ff]purple line[/color] is [color=#9900ff]tangent[/color] to the circle in the [color=#ff00ff]point B[/color] and[color=#6aa84f] segment AB[/color] is the [color=#6aa84f]radius [/color]of the circle. Move the point B around the circle and answer the questions below.[b][br][br] a)[/b] What do you notice?[br][br][b] b) [/b]Conjecture (idea for what the rule might be):[br][br][b] c) [/b]Justification (using rules you already know):

Circle Theorem 6: Angles and Tangents of a Circle

[b]7) [/b] Observe the two tangents [color=#ff00ff][b]DB[/b][/color] and [color=#9900ff][b]CD[/b][/color] drawn from an external point D to the circle passing by points [color=#ff00ff][b]B [/b][/color]and [color=#9900ff][b]C[/b][/color][color=#ff0000]. [/color]Move the slider and answer the questions below.[br][b][br] a) [/b]What do you notice?[br][br][b] b) [/b]Conjecture (idea for what the rule might be):[br][br][b] c) [/b]Justification (using rules you already know):