Circlegeo

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Circlegeo

  1. 1. CIRCLE GEOMETRY Chenda Bun, Kasey La, Ardia Sarao
  2. 2. DEFINITIONS   Circle – A set of points of equal distance from the center.   Circumference – The perimeter of the circle.   Diameter– A chord that passes through the centre.   Radius – Half of the diameter.   Chord – A line segment that joins two points on the circle.
  3. 3.   Tangent - A straight line that touches the circle at a single point.   Arc – Any part of a curve of a circle.   Major Arc – The larger arc.   Minor Arc – The smaller arc.   CentralAngle – An angle that has it’s vertex at the center, two radii form the arms of the angle
  4. 4.   Inscribed Angle – An angle that has it’s vertex on the circle and two chords form the arms.   Intercepted Arc - That part of a circle that lies between two lines that intersect it.   Subtended – Closed off by an arc or line   Segment – A part of a line or curve between two points.   Cyclic Quadrilateral - A quadrilateral whose vertices all lie on a single circle.
  5. 5. RULE #1   The perpendicular line from the centre of a circle to a chord bisects the chord.
  6. 6. RULE #2   Aninscribed angle is subtended by a diameter than all the angles should equal to 90° 90° 90° 90° 90°
  7. 7. RULE #3   If an inscribed angle and a central angle are subtended by the same arc then the inscribed angle is half the central angle. 68° 24° 48° 24° back
  8. 8. RULE #4   All perpendicular bisectors pass through the center. Both are diameters of the circle.
  9. 9. RULE #5   Whentwo or more inscribed angles are subtended by the same arc then all angles are the same. 40° 20° 40°
  10. 10. RULE #6   If two chords in a circle are parallel then they share the same angles. 30° 30° 50° 50° 50° 50° 30° 30°
  11. 11. RULE #7   Iftwo tangents are drawn from a common point, exterior to a circle then the length of the tangent lines should be the same. 90° 90°
  12. 12. RULE #8   When two angles are opposite from each other in a cyclic quadrilateral, then they should be supplementary. 70° 84° <ABC + CDA = 180° 96° + 84° = 180° <BCD + <DAC = 180° 110° + 70° = 180° 110° 96° back
  13. 13. RULE #9   Whenan angle is formed between a tangent line and a chord then it is equal to the inscribed angle on the opposite side of the chord. 70°
  14. 14. RULE #10   Aconvex polygon with n sides can be divided into (n-2) triangles # OF TRIANGLES = n-2 SUM OF INTERIOR <‘s # OF TRIANGLES = 5-2 = 180(n-2) # OF TRIANGLES = 3 =180(5-2) =180(3) =540   The sum of the interior angles of a polygon with n sides = 180(n-2)
  15. 15. PRACTICE QUESTIONS   Definitions   What is the distance from the centre of a circle to a point on the circumference called?   What do you call a line that joins two points on the circumference of a circle but does not pass through the centre?
  16. 16. PRACTICE ANSWERS  Radius  Chord
  17. 17. PRACTICE QUESTIONS   Angles What is the value of X? 30° x Hint
  18. 18. PRACTICE QUESTIONS   Angles Find the angle CDE A B F 93° E 117° C 48° D Hint
  19. 19. PRACTICE QUESTIONS   Angles Find x and y. 35° y° x°
  20. 20. HELPFUL LINKS AND VIDEOS   http://www.mathopenref.com/ arccentralangletheorem.html   http://www.mathopenref.com/chord.html   http://library.thinkquest.org/20991/geo/ circles.html   http://www.coolmath.com/reference/circles- geometry.html   http://www.youtube.com/watch?v=E2uoEMwuyak   http://www.youtube.com/watch?v=ma0qXCyxiQo   http://www.youtube.com/watch?v=4Y9D0v0x4H8
  21. 21. BIBLIOGRAPHY   www.purplemath.com   http://www.mathopenref.com   http://library.thinkquest.org/20991/geo/ circles.html

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