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Circle theorem powerpoint

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Circle theorem powerpoint

  1. 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. 2. Name parts of a circle
  3. 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. 4. This rule can be hard to spot…..
  5. 5. MUST BE THE 1150 CENTER 2300THIS IS THE ONE MOST PEOPLE DON’T SEE......
  6. 6. 800 400 LOOKS DIFFERENT BUT STILL THE CENTRE
  7. 7. 900 1800SPECIAL CASE OF THE SAME RULE……… BUTMAKES A RULE IN ITS OWN RIGHT!!
  8. 8. 900THEOREM 2: Every angle at the circumferenceof a SEMICIRCLE, that is subtended by thediameter of the semi-circle is a right angle.
  9. 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. 10. Now have a go at Worksheet 1 
  11. 11. PALE BLUE AREA IS THE SEGMENTRULE 4: Angles at the circumference in thesame SEGMENT of a circle are equal
  12. 12. PALE BLUE AREA IS THE SEGMENTRULE 4: Angles at the circumference in thesame SEGMENT of a circle are equal
  13. 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. 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. 15. Theorem 5 – A tangent isperpendicular to a radius 900 radius
  16. 16. Theorem 6 – Tangents to a circle from the same point are equal in length
  17. 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. 18. Theorem 5&7 – combined can help you find the missing angles….. 900 x 350 0 70 y 350 900
  19. 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. 20. Have a go at worksheet 2 
  21. 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. 22. Theorem 9 – Alternate angle theorem
  23. 23. Theorem 9 – Alternate angle theoremThe angle between a tangent and a chordIs equal to the angle in the alternate segment
  24. 24. Theorem 9 – Alternate angle theoremThe angle between a tangent and a chordIs equal to the angle in the alternate segment
  25. 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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