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?
