Transcript Circles - Weebly

Circle
Circle Definition
Circle : The set of points coplanar points equidistant from a
given point.
The given point is called the CENTER of the circle.
The distance from the center to the circle is called the RADIUS.
Center
Radius
Definitions
Chord : The segment whose endpoints lie on the circle.
Diameter : A chord that contains the center of the circle.
Tangent : A is a line or line segment that touches a circle at
one point only .
Point of Tangency :
The point where the tangent line
intersects the circle.
Secant : A line that intersects a circle
at two points. It is a line, ray,
or segment that contains a
chord of a circle.
Diameter
Secant
Definitions
Congruent Circles :
Circles that have congruent radii.
2
2
Concentric circles : Circles that lie in the same plane and
have the same center.
Polygons
Inscribed Polygon:
A polygon inside the circle whose
vertices lie on the circle.
Circumscribed Polygon :
A polygon whose sides are
tangent to a circle.
ARCS
Arcs : The part or portion on the circle from some point B
to C is called an arc.
B
C
A
If a circle is divided into two
unequal parts, the longer arc is
called the major arc and the
shorter arc is called the minor
arc.
An angle with its vertex on a circle that is
formed by two other points on the circle is
called an inscribed angle.
For an inscribed angle with the same endpoints
as a central angle, the inscribed angle is half
the central angle.
If arc Q is 3 cm long in the circle above, and the
circumference of the circle is 9 cm, then what is
the measurement of the central angle?
3 cm/9 cm = 1/3
The central angle will be the same
fraction of 360°.
(All circles measure 360°.).
Therefore, set up a ratio to solve
for the central angle
measurement.
The central
angle equals
120°.
1/3 = X/360°
1/3 = 120°/360°
In the circle above, arc Q is 30 mm long. The
circumference of the circle is 90 mm. What is the
measurement of the central angle?
30 mm / 90 mm = 1/3
The central angle will be the same
fraction of 360°.
(All circles measure 360°.).
Therefore, set up a ratio to solve
for the central angle
measurement.
The central
angle equals
120°.
1/3 = X/360°
1/3 = 120°/360°
Given a circle with center B and ABC = 74°,
determine the measure of AKC.
Central
Angle
Inscribed
Angle
For an inscribed angle with the
same endpoints as a central
angle, the inscribed angle is half
the central angle.
AKC = 1/2 × ABC
= 1/2 × 74° = 37°
The Angle
AKC = 37°.
Segment AC is the diameter of the circle.
If the length of segment BD = 7 inches, find
the length of segment BE.
Segment DE is perpendicular to
the diameter AC.
7
??
Therefore, segment DE is
bisected by segment AC.
So, the length of segment BE is
equal to the length of segment
DB.
BE = 7 inches