Circle facts and theorems

Circle Theorem 1

Move points A, B and C on the circumference.[br]The pink lines are radii.[br]What do you notice about the angles? [br][br]Conjecture (idea for what the rule might be):[br][br][br]Justification (using rules you already know):

Circle Theorem 2

Move points A, B and C on the circumference and look at how the angles change.[br]Is it possible to make one of the angles = 90 degrees?[br][br]Conjecture (idea for what the rule might be):[br][br][br]Justification (using rules you already know):

Circle Theorem 3

Move any of the points on the circumference. [br]What do you notice about the 2 angles shown?[br][br]Conjecture (idea for what the rule might be):[br][br][br]Justification (using rules you already know):

Circle Theorem 4

Move any of the points on the circumference.[br]What do you notice about the angles? (hint: look at angles opposite each other)[br][br]Conjecture (idea for what the rule might be):[br][br][br]Justification (using rules you already know):

Circle Theorem 5

Move any of the points on the circumference. [br]The blue line is a tangent to the circle. [br]What do you notice about the angles?[br][br]Conjecture (idea for what the rule might be):[br][br][br]Justification (using rules you already know):

As an extension can you represent your rules in algebraic form? (write them down on paper)