Circles and Angles 1
Compare the angle at the centre to the angle on the circle. Move the points and become familiar with different versions of the diagram.
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Circles and Angles 2
Compare the angle at the centre to the angle on the circle (obtuse and reflex angles). Move the points and become familiar with different versions of the diagram.
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Circle Theorems - angles on the same arc
Investigate angles on the same arc. Move the points - what do you notice?
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Angle in a Semi-circle 1
Move point A or D. What do you notice about the angles?
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Angle in a Semi-circle 2
Angle in a semi-circle -proof.
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Circle theorems - Cyclic Quadrilaterals
Move point A or C. What do you notice about the angles?
Move point B or D. What do you notice? Can you explain these results?
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Circle theorems - Cyclic quadrilaterals
Look at the angles on each arc separately.
Look at both at the same time and move the points.
What do you notice?
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Cyclic Quadrilateral 3
This shows how both pairs of opposite angles in a cyclic quadrilateral sum to 180°
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