Transcript Circles - New Paltz Central School District

Circles
Basic vocabulary
History of the Circle
• The circle has been known since before the
beginning of recorded history. It is the basis
for the wheel, which, with related inventions
such as gears, makes much of modern
civilization possible. In mathematics, the
study of the circle has helped inspire the
development of geometry and calculus.
• Early science, particularly geometry and
Astrology and astronomy, was connected to
the divine for most medieval scholars, and
many believed that there was something
intrinsically "divine" or "perfect" that could
be found in circles.
What is a circle?
• A circle is a locus of a
point in a plane which
moves such that its
distance from a fixed
point in the same plane
remains constant.
• The fixed point is called
the center of the circle
and the fixed distance is
called the radius.
O
Here O is the center
and OP is the radius.
Naming a Circle
Circle F
F
F
center
Use the center to name a circle.
Parts of a Circle
chord
tangent
diameter
radius
Segments & Lines
secant
Let’s review
• The distance across a circle through the
center is called the diameter.
• Radius: is the distance from the center
to any point on the circle. It is half the
diameter.
• Chord: A line segment linking any two
points on a circle
• Tangent: A line passing a circle and
touching it at just one point.
• Secant: A line that intersects a circle at
two points.
Formulas
• Radius/diameter
r = 1/2d and d=2r
• Area
A=
2
∏r
• Circumference
C = 2∏r
or
C = ∏d
Types of Arcs
major arc
M
MNO
minor arc
P
MO
semicircle
MON
O
N
Types of Angles
Central angle
- Vertex is on the center.
Inscribed angle
- Vertex is on the circle.
Circle folding activity
Measure of Arcs & Angles
minor arc = its central angle
major arc = 360 - its central angle
68°
360 – 68 = 292
292°
68°
Measure of Arcs & Angles
minor arc = its central angle
major arc = 360 - its central angle
semicircle = 180
180°
Measure of Arcs & Angles
minor arc = its central angle
major arc = 360 - its central angle
semicircle = 180
inscribed angle
= ½minor arc
68°
34°
SECTOR
Corresponding to a given arc, the
region bounded by the two radii and the
arc itself.