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- 1. Circle Theorem Remember to look for “basics” •Angles in a triangle sum to 1800 •Angles on a line sum to 1800 •Isosceles triangles (radius)•Angles about a point sum to 3600
- 2. Name parts of a circle
- 3. MUST BE THE CENTER 400 800THEOREM 1: ANGLE at the CENTREof the CIRCLE is twice the angle at thecircumference subtended by the samearc
- 4. This rule can be hard to spot…..
- 5. MUST BE THE 1150 CENTER 2300THIS IS THE ONE MOST PEOPLE DON’T SEE......
- 6. 800 400 LOOKS DIFFERENT BUT STILL THE CENTRE
- 7. 900 1800SPECIAL CASE OF THE SAME RULE……… BUTMAKES A RULE IN ITS OWN RIGHT!!
- 8. 900THEOREM 2: Every angle at the circumferenceof a SEMICIRCLE, that is subtended by thediameter of the semi-circle is a right angle.
- 9. CYCLIC QUADRILATEARAL MUST touch the circumference at all four vertices 890 1100 700 910THEOREM 3: Opposite angles sum to 180 in acyclic quadrilateral
- 10. Now have a go at Worksheet 1
- 11. PALE BLUE AREA IS THE SEGMENTRULE 4: Angles at the circumference in thesame SEGMENT of a circle are equal
- 12. PALE BLUE AREA IS THE SEGMENTRULE 4: Angles at the circumference in thesame SEGMENT of a circle are equal
- 13. THEOREM 4: Angles at the circumference inthe same SEGMENT of a circle are equalNOTE: Will lead you to SIMILAR triangles (oneis an enlargement of the other….)
- 14. • A tangentthe line thatof tangents andone Enter is a world touches a circle at point only. This chords….. the point of point is called contact.• A chord is a line that joins two points on the circumference.
- 15. Theorem 5 – A tangent isperpendicular to a radius 900 radius
- 16. Theorem 6 – Tangents to a circle from the same point are equal in length
- 17. Theorem 7 – The line joining an external point to thecentre of a circle bisects the angle between the tangents 350 0 70 350
- 18. Theorem 5&7 – combined can help you find the missing angles….. 900 x 350 0 70 y 350 900
- 19. Theorem 8 – A radius bisects a chord at 900 MIDPOINT OF THE CHORD chord 900And the chord will be cut perfectly in half!!!
- 20. Have a go at worksheet 2
- 21. Theorem 9 – Alternate angle theorem Need a tangentAnd a triangle that joins the tangent and two other points on the circumference of the circle
- 22. Theorem 9 – Alternate angle theorem
- 23. Theorem 9 – Alternate angle theoremThe angle between a tangent and a chordIs equal to the angle in the alternate segment
- 24. Theorem 9 – Alternate angle theoremThe angle between a tangent and a chordIs equal to the angle in the alternate segment
- 25. COMMON EXAM ERROR! IT TOONLY A IS IS THINK DIAMETER THIS IS A IF YOU ARE DIAMETER – TOLD SO… SO.. THIS MUST READ BE 900 – QUSETIONS “TANGENT CAREFULLY.. MEETS RADIUS”

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