Circle theorems

ForfatterZoë Carolan, Jasmine Vincent, Valeria Cipolli Kumoto, PCARTS, Brigitte Gudz, Hillmath, Aidan Pittman, James Monaghan, Brenden, JCarpenter2, NABILAH FARHANA BINTI YAHYA, Jonathan Longstaffe, Caribou Contests

Emne:Cirkel

Circle Theorem 1: Angle at the Centre

1) The central angle A and the inscribed angle E are related to the green arc CBD. Move the points C, D, and E to explore the model and then answer the questions below.

a) Write down what you notice about the relationship between the two angles.  b) Conjecture (idea for what the rule might be):  c) Justification (using rules you already know):

Circle Theorem 2: Angles in a semicircle

2) The diameter CD divides the circumference into two equal parts (semicircles). The inscribed angle E is subtended (related) by the green arc CBD. Move point E around the circumference and then move the diameter BD as well. Explore and answer the questions below.

a) Write down what you notice?  b) Conjecture (idea for what the rule might be):  c) Justification (using rules you already know):

Circle Theorem 3: Inscribed angles subtended by the same arc

3) The inscribed angles B and D are subtended by the same pink arc AEC. Move the points around the circumference and then answer the questions below.  a) What do you notice?  b) Conjecture (idea for what the rule might be):  c) Justification (using rules you already know):

Circle Theorem 4: Cyclic quadrilateral

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

Circle Theorem 5: Alternate Segment Theorem

5) Observe the angles between the chord BA and chord CA and atangent passing through point A. Move the points A, B, and C around the circumference and answer the questions below.  a) What do you notice?  b) Conjecture (idea for what the rule might be):  c) Justification (using rules you already know):

Circle Theorem 6: Tangent on a Circle (Tangent and Radius)

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

Circle Theorem 7: Angles and Tangents of a Circle

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

Circle Theorem 8: Radius and Chord

8) Observe the chord CD and the radius AF. Move the points C and D around the circumference.  a) What do you notice?  b) Conjecture (idea for what the rule might be):  c) Justification (using rules you already know):

Extra - Circle Theorem 9: Intersecting Chord

9) Observe the two chords CD and EF. Move the points C, D, E, and F around the circumference and answer the questions below.  a) What do you notice?  b) Conjecture (idea for what the rule might be):  c) Justification (using rules you already know):