CIRCLE GEOMETRY Chenda Bun, Kasey La, Ardia Sarao
Circlegeo
Sep 01, 2014
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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