CIRCLE GEOMETRY Chenda Bun, Kasey La, Ardia Sarao

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.

 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.

 Central Angle – An angle that has it’s vertex at the center, two radii form the arms of the angle

  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.

RULE #1

 The perpendicular line from the centre of a circle to a chord bisects the chord.

RULE #2

 An inscribed angle is subtended by a diameter than all the angles should equal to 90°

90°

90°

90°

90°

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

RULE #4

 All perpendicular bisectors pass through the center. Both are diameters of the circle.

RULE #5

 When two or more inscribed angles are subtended by the same arc then all angles are the same.

40°

40°

20°

RULE #6

  If two chords in a circle are parallel then they share the same angles.

50°

50°

50°

50°

30°

30°

30°

30°

RULE #7

  If two tangents are drawn from a common point, exterior to a circle then the length of the tangent lines should be the same.

90°

90°

RULE #8

 When two angles are opposite from each other in a cyclic quadrilateral, then they should be supplementary.

70°

110°

96°

84° <ABC + CDA = 180° 96° + 84° = 180°

<BCD + <DAC = 180° 110° + 70° = 180°

back

RULE #9  When an 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°

RULE #10  A convex polygon with n sides can be divided into

(n-2) triangles

 The sum of the interior angles of a polygon with n sides = 180(n-2)

# OF TRIANGLES = n-2 # OF TRIANGLES = 5-2 # OF TRIANGLES = 3

SUM OF INTERIOR <‘s = 180(n-2) =180(5-2) =180(3) =540

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?

PRACTICE ANSWERS

 Radius

 Chord

PRACTICE QUESTIONS

 Angles

30°

x

What is the value of X?

Hint

PRACTICE QUESTIONS

 Angles Find the angle CDE

93°

117°

A B

C

D

E

F

Hint

48°

PRACTICE QUESTIONS

 Angles

35°

x°

y°

Find x and y.

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

BIBLIOGRAPHY

 www.purplemath.com  http://www.mathopenref.com  http://library.thinkquest.org/20991/geo/

circles.html