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Circle theorems
Circle theorems are rules about angles in circles. Learn each one with its reason, because the reason earns marks.
The theorems
Using them
Look for the shapes: a triangle with a diameter as one side, four points on the circle, an arrow shape from the centre, a tangent.
Writing reasons
Always state the theorem in words, for example "opposite angles in a cyclic quadrilateral add up to 180°".
The angle at the centre is 140°. Find the angle at the circumference standing on the same arc.
- The angle at the centre is twice the angle at the circumference.
- 140 ÷ 2
Answer: 70°
Centre angle is double the circumference angle; semicircle angle 90°; same segment angles equal; cyclic quadrilateral opposites add to 180°; tangent meets radius at 90°.
The interactive lesson includes the diagrams for this topic.
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