1. 28. Circle Theorems

2. Circle Theorems
Assumed knowledge
recall the definition of a circle and identify (name) and draw the parts of a circle
understand related terms of a circle
draw a circle given the radius or diameter
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3. Circle theorems learning objectives:
find missing angles on diagrams (31.1 and rest of chapter)
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4. Circle theorems - Tangents
learning objectives:
understand and use the fact that the tangent at any point on a circle is perpendicular to the radius at that point (31.2)
understand and use the fact that tangents from an external point are equal in length
(31.2)
give reasons for angle calculations involving the use of tangent theorems (31.2)
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5. Circle theorems learning objectives: Prove and use the facts that
the angle subtended by an arc at the centre of a circle is twice the angle subtended at any point on the circumference (31.3)
the angle in a semicircle is a right angle (31.3)
the perpendicular from the centre of a circle to a chord bisects the chord (31.3)
the angles in the same segment are equal (31.4)
opposite angles in a cyclic quadrilateral sum to 180° (31.4)
alternate segment theorem (31.4)
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6. Your turn