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- 1. CIRCLE GEOMETRY Chenda Bun, Kasey La, Ardia Sarao
- 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. 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. 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. RULE #1 The perpendicular line from the centre of a circle to a chord bisects the chord.
- 6. RULE #2 Aninscribed angle is subtended by a diameter than all the angles should equal to 90° 90° 90° 90° 90°
- 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. RULE #4 All perpendicular bisectors pass through the center. Both are diameters of the circle.
- 9. RULE #5 Whentwo or more inscribed angles are subtended by the same arc then all angles are the same. 40° 20° 40°
- 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. 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. 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. 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. 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. 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. PRACTICE ANSWERS Radius Chord
- 17. PRACTICE QUESTIONS Angles What is the value of X? 30° x Hint
- 18. PRACTICE QUESTIONS Angles Find the angle CDE A B F 93° E 117° C 48° D Hint
- 19. PRACTICE QUESTIONS Angles Find x and y. 35° y° x°
- 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. BIBLIOGRAPHY www.purplemath.com http://www.mathopenref.com http://library.thinkquest.org/20991/geo/ circles.html

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